
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
Let the function $f(x)=2\sin \left( \frac {\pi}{2}+x\right)\cos x- \sqrt {3}(\cos x-\sin x)^{2}$.  
$(1)$ Find the interval of monotonic decrease for the function $f(x)$;  
$(2)$ Move the graph of $f(x)$ to the right by $\frac {\pi}{12}$ units, then shrink the x-coordinates of all points on the graph to half of their original values to obtain the function $y=g(x)$. Calculate the value of $g\left( \frac {\pi}{4}\right)$.

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