
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  $1 = x_{1} < x_{2} < \dots < x_{k} = n$  denote the sequence of all divisors  $x_{1}, x_{2} \dots x_{k}$  of  $n$  in increasing order. Find the smallest possible value of  $n$  such that  $$ n = x_{1}^{2} + x_{2}^{2} +x_{3}^{2} + x_{4}^{2}. $$  *Proposed by Justin Lee*

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