
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
Let \( x_1, x_2, \ldots, x_{10} \) be non-zero integers satisfying \( -1 \leq x_i \leq 2 \) for \( i = 1, 2, \ldots, 10 \). If \( x_1 + x_2 + \ldots + x_{10} = 11 \), find the maximum possible value for \( x_1^2 + x_2^2 + \ldots + x_{10}^2 \).

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