[X] Plan Double Break
I see two main arguments against double breakthough: first, the argument that it's not super likely to succeed, and second, the argument that it's further down the priority list than social actions. I don't find either very convincing.
First, the 'statistical' argument of 'oh only 17% chance of success' is basically nonsense. It's based on some misbegotten assumption that 'success' is defined as a double breakthrough, but the plan only really wants 'at least one' breakthrough. To be realistic about it, this is about a 66% chance of 'success'. Double Break's not depending on an actual double breakthrough despite the name. Also, any breakthrough action anytime will have the same chance of success. To do one breakthrough attempt one week and one breakthrough attempt the next is identical to doing two at once. (Ignoring the possibility of a 'recent conflict' bonus, but that's Magical Christmasland thinking, so it's not a real argument anyway even if it's in my favor.)
There's also a subargument 'but what if we fail and lose progress' which is also, to put it lightly, silly. It will apply no matter when Ling Qi attempts breakthrough and it's not something affected by the timing of her attempts. BESIDES the fact that cultivation actions benefit most from consolidation and grouped-up efforts, doing everything possible in a single week in order to benefit from pills and bonuses and whatnot. To do one breakthrough this week and another next, with the intention of alternating attempts with actions to reach/rereach peak is what's actually 'inefficient' in cultivation conceptual terms.
This is, of course, ignoring social, which brings me to the second primary argument against Double Break: the argument of prioritisation.
So second: no, I don't think that social is a priority. There are no ticking timebombs or must-takes that significantly improve Ling Qi's ability to act or improve her number of choices. The 'advice' actions offered are slow on return and honestly are not all that actionable—I'll tell you what Han Jian will say. He'll give advice to stay away from Liling vs. Meizhen, a short biography of the concerning new threat Kang Zihao, the interests of the Kang family if Ling Qi doesn't figure them out on her own, and Cai Renxiang's interest in stopping silliness/blatant banditry. Meizhen will say 'get to Silver or Yellow, that's a sure way to protect yourself from scrubs and will let you compete with the stronger ones'. Or maybe I'm really wrong and someone will say 'don't breakthrough too early or it'll get you in the spotlight', except that's not going to happen because this is Xianxia and it's all about moving up as fast as possible. But no matter what they say, all that they will give is information (and maybe a roll or short-term bonus on something as a gimme to keep Ling Qi moving).
Information about others is not useful to Ling Qi because Ling Qi's goals for the next month are entirely self-interested: breakthrough. Meizhen said 'if you wanna help me become competitive in my arena'. Han Jian and Gu Xiulan and Han Fang (and maybe Fan Yu, who knows), all of them are moving up to Yellow and Silver, and Kang Zihao and Cai Renxiang and Gan Guangli are all Yellow and Silver already. These are the names that Ling Qi knows because they're the characters that matter in her quest to the top. If her life was a sports anime these would be the broad backs that Ling Qi strives to compete with. If there is any action that will improve Ling Qi's ability to compete or continue to progress as she has, it is either going to the Archive and mastering some Arts or breaking through, and no leading plan has included the Archives. So we can't chew gum, I guess.
Worry about optics all you like—Ling Qi's already won that in the Thunderdome. Dislike to Wary, and having Cai Renxiang, the girl borrowing the image of Satsuki Kiryuin, declare your most optics focused opponent a bandit, and coming out of beating someone who 'should' beat you easily while having a noble declare you her friend, and doing it while fabulous in new clothes—coming from an urchin, that's outright shock and awe. Proponents of social say, 'Thunderdome gave us breathing room and now we aren't under threat, so we can coast a bit and chat'. No. We've got breathing room socially so we have to push in the other arenas Ling Qi is involved in. Shock and Awe is an approach about momentum. Under the social plans, more than 50% of the time Ling Qi staggers in her cultivation. Yes, social is a power all its own, but it's only obvious to people who already know about it, and the only people who know everything about Ling Qi's social circles are the readers and Ling Qi. And maybe Huang Da.
To sum up: to put breakthrough off for 'fear of failing' is absurd because it is as if you are running and come across a gap, and decide to not jump over the gap. The gap is not getting any smaller any time soon and no one is going to build a suspension bridge for you to walk across it easily. To put breakthrough off for 'fear of someone walking up behind you and pushing you into the gap' is possibly even more absurd. You could have just jumped already. You don't stop to tiptoe to the edge for a long jump. You run.
(on another note: I really love how a throwaway word used by Alectai became the thread standard for the event of the breaking of the truce, even to the point that it's the threadmark title for the updates)