
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 $150$ is chosen in such a way that if $n \leq 100$, then the probability of choosing $n$ is $p$, and if $n > 100$, then the probability of choosing $n$ is $5p$. The probability that a perfect square is chosen is what?
A) 0.04857
B) 0.05714
C) 0.06571
D) 0.07429

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