
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 define the function $f(x)= \overrightarrow{m}\cdot \overrightarrow{n}$.
1. When $x=\pi$, find the value of the function $f(x)$.
2. Given a triangle $ABC$ with angles $A$, $B$, $C$ opposite to sides $a$, $b$, $c$ respectively, and satisfying $b\cos C+ \frac{1}{2}c=a$, find the size of angle $B$ in triangle $ABC$.

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