
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 $a\_n=n^{2}(\cos ^{2} \frac {nπ}{3}-\sin ^{2} \frac {nπ}{3})$. Let $S\_n$ denote the sum of the first $n$ terms.
(1) Find $S\_n$;
(2) Let $b\_n= \frac {S\_{3n}}{n\cdot 4^{n}}$, find the sum of the first $n$ terms of the sequence $\{b\_n\}$, denoted as $T\_n$.

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