
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 \( x_{1}, x_{2}, \cdots, x_{40} \) are all positive integers, and
\[
x_{1} + x_{2} + \cdots + x_{40} = 58.
\]

If the maximum value of \( x_{1}^{2} + x_{2}^{2} + \cdots + x_{40}^{2} \) is \( A \) and the minimum value is \( B \), then \( A + B = \).

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