
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 vectors $\overrightarrow{m} = (\sin \frac{x}{4}, \cos \frac{x}{4})$ and $\overrightarrow{n} = (\sqrt{3}\cos \frac{x}{4}, \cos \frac{x}{4})$, let $f(x) = \overrightarrow{m} \cdot \overrightarrow{n}$.
(1) If $f(x) = 1$, find the value of $\cos(x + \frac{\pi}{3})$;
(2) In $\triangle ABC$, where the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and it satisfies $(2a-c)\cos B = b\cos C$, find the magnitude of angle $B$ and the range of values for the function $f(A)$.

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