
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 $a\_n=2n\cdot (\cos ^{2} \frac {nπ}{3}-\sin ^{2} \frac {nπ}{3})$, and its sum of the first $n$ terms is denoted as $S\_n$. Find the value of $S\_{30}$.

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