
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  $13$  marbles that are labeled with positive integers such that the product of all  $13$  integers is  $360$ . Moor randomly picks up  $5$  marbles and multiplies the integers on top of them together, obtaining a single number. What is the maximum number of different products that Moor can obtain?

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