
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
Let $\overrightarrow{m} = (\sqrt{3}\sin \frac{x}{4}, 1)$ and $\overrightarrow{n} = (\cos \frac{x}{4}, \cos^2 \frac{x}{4})$, and the function $f(x) = \overrightarrow{m} \cdot \overrightarrow{n}$.
(1) When $x = \pi$, find the value of the function $f(x)$;
(2) Given that in $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and it satisfies $b\cos C + \frac{1}{2}c = a$, find the magnitude of angle $B$ in $\triangle ABC$.

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