
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 is solving a math problem, and he encounters the expression  $\sqrt{15!}$ . He attempts to simplify this radical as  $a\sqrt{b}$  where  $a$  and  $b$  are positive integers. The sum of all possible 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