
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
The set \( M \) consists of \( n \) numbers, where \( n \) is odd and \( n > 1 \). The set has the property that if any element of it is replaced by the sum of the other \( n-1 \) elements, the total sum of all \( n \) elements does not change. Find the product of all \( n \) elements in the set \( M \).

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