
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 sequence $\{a_n\}$ that satisfies $a_{n+2} - a_{n+1} = a_{n+1} - a_{n}$, where $n \in \mathbb{N}^+$, and $a_5 = \dfrac{\pi}{2}$. If the function $f(x) = \sin(2x) + 2\cos^2\left(\dfrac{x}{2}\right)$, and the sequence $\{b_n\} = f(a_n)$, then the sum of the first 9 terms of $\{b_n\}$ is $\_\_\_\_\_\_\_\_\_\_$.

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