
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 $200$ is chosen such that if $n \leq 100$, then the probability of choosing $n$ is $p$, and if $n > 100$, then the probability of choosing $n$ is $2p$. Determine the probability that a perfect square is chosen.
A) $\frac{1}{50}$
B) $\frac{1}{30}$
C) $\frac{1}{25}$
D) $\frac{1}{20}$
E) $\frac{1}{15}$

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