
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 the sequence ${a_{n}}$ is an arithmetic sequence with $a_{11} = \frac{\pi}{2}$, and the function $f(x) = \sin(2x) + 2\cos^2\left(\frac{x}{2}\right)$, let $b_{n} = f(a_{n})$. Calculate the sum of the first 21 terms of the sequence ${b_{n}}$.

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