
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
In $\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to $\angle A$, $\angle B$, and $\angle C$ respectively, and $a$, $b$, and $c$ form an arithmetic sequence.
(1) Find the maximum value of $\angle B$, denoted as $B\_0$.
(2) Under the condition of (1), find the monotonically decreasing interval and the extreme values of the function $f(x) = \sin(2x + B\_0) + \sqrt{3} \cos(2x + B\_0)$ on the interval $[0, \pi]$.

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