
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 the equation $k^2_1 + k^2_2 + ... + k^2_n = 2002$, determine the maximum value of $n$ for which the sum of squares of $n$ distinct positive integers is equal to $2002$.

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