
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 the function \( f(x) = x^2 - 2 \ln x \), if there exist \( x_1, x_2, \cdots, x_n \in \left[ \frac{1}{\mathrm{e}}, \mathrm{e} \right] \) such that \( f(x_1) + f(x_2) + \cdots + f(x_{n-1}) = f(x_n) \) holds, find the maximum value of \( n \).

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