
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
A number from 1 to 144 is hidden. You are allowed to define a subset of the set of numbers from 1 to 144 and ask whether the hidden number belongs to this subset. For an affirmative answer, you must pay 2 rubles; for a negative answer, you must pay 1 ruble. What is the...

Present the answer in LaTex format: \boxed{Your answer}
user