
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 chosen. You are allowed to select one subset from the set of numbers from 1 to 144 and ask whether the chosen number is in that subset. For a "yes" answer, you pay 2 rubles; for a "no" answer, you pay 1 ruble. What is the minimum amount of money necessary to guarantee guessing the number correctly?

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