
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 positive integer $n$ not exceeding $120$ is chosen such that if $n \leq 60$, the probability of choosing $n$ is $p$, and if $n > 60$, the probability is $2p$. Additionally, if $n$ is even, the probability of choosing $n$ doubles. The probability that a perfect square is chosen is to be calculated.
**A)** 0.06  
**B)** 0.065  
**C)** 0.074  
**D)** 0.08  
**E)** 0.1

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