
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
Consider a permutation $\left\{a_{1}, a_{2}, \ldots, a_{n}\right\}$ of $\{1,2, \ldots, n\}$. If at least one of $a_{1}, a_{1}+a_{2}, a_{1}+a_{2}+a_{3}, \ldots, a_{1}+a_{2}+\ldots+a_{n}$ is a perfect square, the permutation is referred to as a "quadratic permutation." Determine all positive integers $n$ for which every permutation of $\{1,2, \ldots, n\}$ is a "quadratic permutation."

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