
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 $f(x)=2\cos (x- \frac {\pi}{3})+2\sin ( \frac {3\pi}{2}-x)$  
$(1)$ Find the interval of monotonic decrease for the function $f(x)$.  
$(2)$ Find the maximum value of the function $f(x)$, and the set of $x$ for which $f(x)$ attains its maximum value.  
$(3)$ If $f(x)= \frac {6}{5}$, find the value of $\cos (2x- \frac {\pi}{3})$.

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