[li]Are there any actions known (and available to a POSI player) that reliably advance "counting the days"? I’ve been holding onto 2 cards related to actions dependent on the days count, but I cannot figure out how to advance it. Is it just a random counter somewhere? Or can I help move it forward by doing something?
Can you say what your level is at? There are a few, but they may not be available if you have the wrong level.
Whichever faction you are closest to has a guaranteed CtD option. There are also storylets scattered around London that do so on specific ranges. Finally, most of Menace reduction cards have CtD options.
I recommend checking the docks, Forgotten Quarter, and University for some.
There is one option in the Flit, if I remember correctly, regarding urchins. My CtD raises so quickly that I rarely bother to seek for those options until it is too late.
I am at 8. I want to cycle it back around to lower numbers.
At that stage if you have certain “closest to” you can go to the Forgotten Quarter and Speak to an Aristocratic Academic (under Seeking Curios and Secrets).
After that there is an option that appears in the Palace (as long as you are not soul-less) and then Shadowy dealings at the University to get it up to 14. Then wait to draw the card to cash it in. After that take a look at dicing in Wolfstack Docks.
Both Docks and Forgotten Quarter options do rely on who you are closest to though so you might not be able to do the whole cycle via the storylets but there are cards.
The guide Wiwo linked is probably your best bet, but Connections and Menace-reduction cards tend to be the main way I progress that particular carousel.