
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 $f(x)=x\cos\frac{{πx}}{2}$. The sequence $\{a_{n}\}$ satisfies $a_{n}=f\left(n\right)+f\left(n+1\right)$ for $n\in N^{*}$. Find the sum of the first $100$ terms of the sequence $\{a_{n}\}$.

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