
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 let  $d_{1},d_{2},,\ldots ,d_{k}$  be its divisors, such that  $1=d_{1}<d_{2}<\ldots <d_{k}=n$ . Find all values of  $n$  for which  $k\geq 4$  and  $n=d_{1}^{2}+d_{2}^{2}+d_{3}^{2}+d_{4}^{2}$ .

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