
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 $f(x)=\cos (2x+ \frac {π}{3})+\sin ^{2}x$.
(1) Find the smallest positive period and the monotonic interval of the function $f(x)$;
(2) Let $a$, $b$, and $c$ be the sides opposite to angles $A$, $B$, and $C$ of an acute triangle $\triangle ABC$, respectively. If $\cos B= \frac {1}{3}$, $c= \sqrt {6}$, and $f( \frac {C}{2})=- \frac {1}{4}$, find $b$.

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