
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 real numbers \( x_{1}, x_{2}, x_{3}, \ldots, x_{n} \) are the consecutive terms of an arithmetic sequence. If

\[ \frac{x_{2}}{x_{1}+x_{3}}+\frac{x_{3}}{x_{2}+x_{4}}+\frac{x_{4}}{x_{3}+x_{5}}+\cdots+\frac{x_{n-2}}{x_{n-3}+x_{n-1}}+\frac{x_{n-1}}{x_{n-2}+x_{n}}=1957 \]

what is the value of \( n \)?

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