
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $2b\cos A=2c-\sqrt{3}a$.
(1) Find $B$;
(2) Define the function $f(x)=\cos x \cdot \sin(x+\frac{\pi}{3})-\frac{\sqrt{3}}{4}$, find the maximum value of $f(A)$.

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