
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
How should the numbers $1, 2, \ldots, 1962$ be arranged in the sequence $a_{1}, a_{2}, \ldots, a_{1962}$ so that the sum $\left|a_{1} - a_{2}\right| + \left|a_{2} - a_{3}\right| + \ldots + \left|a_{1961} - a_{1962}\right| + \left|a_{1962} - a_{1}\right|$ is maximized?

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