
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
Christina and Alex play a game in which Christina picks an integer between 1 and 360 inclusive and Alex multiplies that integer with a factor such that the product is equal to 360. How many integers can Christina pick for which this operation is possible, and what is the sum of all such integers?

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