
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
Given a positive integer \( n \) (where \( n > 1 \)), and \( n \) real numbers \( x_{1}, x_{2}, \ldots, x_{n} \) that satisfy \( x_{1}, x_{2}, \ldots, x_{n} \in [0, n] \) and
\[
x_{1} x_{2} \cdots x_{n} = \left(n - x_{1}\right) \left(n - x_{2}\right) \cdots \left(n - x_{n}\right),
\]
determine the maximum value of \( y = x_{1} + x_{2} + \cdots + x_{n} \).

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