
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 that $S_{n}$ is the sum of the first $n$ terms of the sequence $\{a_{n}\}$, $a_{1}=1$, and $a_{n}\cdot a_{n+1}+\cos \left(n\pi \right)=\sin (n\pi -\frac{π}{2})$, calculate the value of $S_{2022}$.

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