
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
Let \( x_{i} \in \{1, 2, \cdots, n\}, \, i = 1, 2, \cdots, n \) satisfy \( \sum_{i=1}^{n} x_{i} = \frac{n(n+1)}{2} \) and \( x_{1} x_{2} \cdots x_{n} = n! \). Then, the largest positive integer \( n \) such that \( x_{1}, x_{2}, \cdots, x_{n} \) must be a permutation of \(\{1, 2, \cdots, n\}\) is _____.

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