
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 $100$ is chosen such that if $n\le 60$, then the probability of choosing $n$ is $q$, and if $n > 60$, then the probability of choosing $n$ is $2q$. Find the probability that a perfect square is chosen.
- **A)** $\frac{1}{35}$
- **B)** $\frac{2}{35}$
- **C)** $\frac{3}{35}$
- **D)** $\frac{4}{35}$
- **E)** $\frac{6}{35}$

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