
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 \( d_{1}, d_{2}, \cdots, d_{k} \) be all the divisors of the positive integer \( n \), denoted as:
\[ 1 = d_{1} < d_{2} < d_{3} < \cdots < d_{k} = n. \]

Find all \( n \) such that \( k \geq 4 \) and \( d_{1}^{2} + d_{2}^{2} + d_{3}^{2} + d_{4}^{2} = n \).

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