
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 \( 2n \) real numbers \( a_1, a_2, \ldots, a_{2n} \) satisfying the condition \(\sum_{i=1}^{2 n-1} (a_{i+1} - a_i)^2 = 1\), find the maximum value of \(\mu = (a_{n+1} + a_{n+2} + \cdots + a_{2n}) - (a_1 + a_2 + \cdots + a_n)\).

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