
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
For all real numbers \( x_{1}, x_{2}, \ldots, x_{60} \in [-1, 1] \), find the maximum value of \( \sum_{i=1}^{60} x_{i}^{2} (x_{i+1} - x_{i-1}) \), where \( x_{0} = x_{60} \) and \( x_{61} = x_{1} \).

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