
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
Consider $15!$ (15 factorial). A positive integer divisor of $15!$ that is also divisible by 13 is chosen at random. What is the probability that this divisor is a perfect square? This probability can be expressed as a fraction $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
A) 18
B) 19
C) 21
D) 22
E) 23

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