
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 function $f(x)=\cos (2x- \frac {2\pi}{3})-\cos 2x$ $(x\in\mathbb{R})$.
- $(I)$ Find the intervals of monotonic increase for the function $f(x)$.
- $(II)$ In triangle $ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $f( \frac {B}{2})=- \frac { \sqrt {3}}{2}$, $b=1$, $c= \sqrt {3}$ and $a > b$, find $B$ and $C$.

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