
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 $n > 1$. It is such that if any element is replaced by the sum of the remaining $n-1$ elements of $M$, the 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}
user