
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 angles $A$, $B$, and $C$ respectively, and $(2a-c) \cos B - b \cos C = 0$.
(1) Find $\angle B$;
(2) Let $f(x) = -2 \cos (2x + B)$. After shifting the graph of $f(x)$ to the left by $\frac{\pi}{12}$, we obtain the graph of $g(x)$. Find the interval(s) where $g(x)$ is increasing.

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