
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
$a_{1}, a_{2}, \ldots a_{100}$ is a permutation of $1, 2, \ldots, 100$. Let $S_{k}=a_{1}+a_{2}+\ldots+a_{k}$. What is the maximum number of perfect squares that can appear among $S_{1}, S_{2}, \ldots, S_{100}$?

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