
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
Anders encounters the expression \(\sqrt{15!}\) and attempts to simplify it into the form \(a \sqrt{b}\) where \(a\) and \(b\) are positive integers. The sum of all possible distinct values of \(ab\) can be expressed in the form \(q \cdot 15!\) for some rational number \(q\). Find \(q\).

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