
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 sum $S_{120}$ of the sequence $\{a_{n}\}$ where $a_{n}=(-1)^{n}(2n-1)\cdot \cos {\dfrac {nπ}{2}}+1$ for all $n \in \mathbb{N}^{*}$, can be determined by evaluating the formula for the sum of the first 120 terms.

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