
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 sequence $1, 2, 3, \cdots, 1962$, find a permutation $a_{1}, a_{2}, a_{3}, \cdots, a_{1962}$ such that the sum:
$$
\left|a_{1}-a_{2}\right|+\left|a_{2}-a_{3}\right|+\cdots+\left|a_{1961}-a_{1962}\right|+\left|a_{1962}-a_{1}\right|
$$
is maximized.

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