
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
Let n be a positive interger. Let n real numbers be wrote on a paper. We call a "transformation" :choosing 2 numbers  $a,b$  and replace both of them with  $a*b$ . Find all n for which after a finite number of transformations and any n real numbers, we can have the same number written n times on the paper.

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