
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 $f(x)=\cos (2x- \frac {π}{3})+2\sin (x- \frac {π}{4})\sin (x+ \frac {π}{4})$.
(1) Find the interval(s) where the function $y=f(x)$ is increasing;
(2) In triangle $ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$, respectively. Given that $c=2 \sqrt {3}$, $f(C)=1$, and point $O$ satisfies $| \overrightarrow{OA}|=| \overrightarrow{OB}|=| \overrightarrow{OC}|$, find the range of values for $ \overrightarrow{CO}\cdot( \overrightarrow{CA}+ \overrightarrow{CB})$.

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