
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 $n$ be a positive integer, and $d_1 < d_2 < d_3 < d_4$ be the four smallest positive integer divisors of $n$. If $n = d_1^2 + d_2^2 + d_3^2 + d_4^2$, find the value of $n$.

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