
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 \( x_{1}, x_{2}, \cdots, x_{n} \) and \( a_{1}, a_{2}, \cdots, a_{n} (n>2) \) be sequences of arbitrary real numbers satisfying the following conditions:
1. \( x_{1}+x_{2}+\cdots+x_{n}=0 \);
2. \( \left|x_{1}\right|+\left|x_{2}\right|+\cdots+\left|x_{n}\right|=1 \);
3. \( a_{1} \geqslant a_{2} \geqslant \cdots \geqslant a_{n} \).

To ensure that the inequality \( \mid a_{1} x_{1}+a_{2} x_{2}+\cdots+a_{n} x_{n} \mid \leqslant A\left(a_{1}-a_{n}\right) \) holds, find the minimum value of \( A \).

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