
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 the planar vectors $\overrightarrow {m}=(2-\sin(2x+ \frac {π}{6})，-2)$ and $\overrightarrow {n}=(1，\sin^{2}x)$, and the function $f(x)= \overrightarrow {m} \cdot \overrightarrow {n}$.
(1) Find the intervals where the function $f(x)$ is monotonically increasing.
(2) In triangle $△ABC$, if the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $f(\frac{B}{2})=1$, $b=1$, and $c=\sqrt{3}$, find the value of $a$.

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