
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
The general term of the sequence $\{a_n\}$ is given by $a_n = n^2(\cos^2 \frac{n\pi}{3} - \sin^2 \frac{n\pi}{3})$. Let $S_n$ denote the sum of the first $n$ terms of this sequence. Find the value of $S_{30}$.

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