
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 $n\le 60$, then the probability of choosing $n$ is $p$, and if $n > 60$, then the probability of choosing $n$ is $2p$. The probability that a perfect square is chosen is?
A) $\frac{1}{180}$
B) $\frac{7}{180}$
C) $\frac{13}{180}$
D) $\frac{1}{120}$
E) $\frac{1}{60}$

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