
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
Given the sequence $\{a_n\}$, if $\frac{a_1^2}{1^2} + \frac{a_2^2}{2^2} + \frac{a_3^2}{3^2} + \ldots + \frac{a_n^2}{n^2} = 4n - 4$ and $a_n \geqslant 0$, calculate the value of $S_{100}$.

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