
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
Calculate the number of possible values of the greatest common divisor when the product of two integers is 360 and their greatest common divisor multiplied by their least common multiple equals the product of the two integers.

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