
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 real numbers \( x_1, x_2, \ldots, x_{2021} \) satisfy \( \sum_{i=1}^{2021} x_i^2 = 1 \), find the maximum value of \( \sum_{i=1}^{2020} x_i^3 x_{i+1}^3 \).

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