
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 function $f(x)=x^{2}\cos \frac {πx}{2}$, the sequence $\{a_{n}\}$ is defined as $a_{n}=f(n)+f(n+1), n\in\mathbb{N}^{*}$. Calculate the sum of the first 100 terms of the sequence $\{a_{n}\}$, denoted as $S_{100}=$ \_\_\_\_\_\_.

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