
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 $\triangle ABC$, $\tan A = -3 \tan B$ and $b \cos C + c \cos B = \sqrt{3} b$.
(1) Find the measure of angle $C$;
(2) Let $f(x) = \sin(x + A) + \cos^2 \left( \frac{x + B}{2} \right)$, where $x \in \left[0, \frac{5 \pi}{6} \right]$, find the range of $f(x)$.

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