
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
Cookie Monster says a positive integer \( n \) is crunchy if there exist \( 2n \) real numbers \( x_1, x_2, \ldots, x_{2n} \), not all equal, such that the sum of any \( n \) of the \( x_i \) 's is equal to the product of the other \( n \) of the \( x_i \) 's. Determine all crunchy integers.

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