
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
Given that \( n \) is a positive integer and \( n \leq 144 \), ten questions of the type "Is \( n \) smaller than \( a \)?" are allowed. The answers are provided with a delay such that the answer to the \( i \)-th question is given only after the \((i+1)\)-st question is asked for \( i = 1, 2, \ldots, 9 \). The answer to the tenth question is given immediately after it is asked. Find a strategy for identifying \( n \).

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