
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 $\overrightarrow{m}=(\sin x,\cos x)$, $\overrightarrow{n}=(\cos x, \sqrt {3}\cos x)$, and the function $f(x)= \overrightarrow{m} \cdot \overrightarrow{n} - \frac{\sqrt{3}}{2}$.
(1) Find the smallest positive period and the monotonically increasing interval of the function $f(x)$;
(2) If the angles $A$, $B$, and $C$ of $\triangle ABC$ correspond to the sides $a$, $b$, and $c$, respectively, and satisfy $b^{2}+c^{2}=a^{2}+ \sqrt {3}bc$, find the value of $f(A)$.

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