
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 $f(x)=2\cos ^{2}x-2\sin (x+ \frac {3}{2}π)\cos (x- \frac {π}{3})- \frac {3}{2}$.
(1) Find the interval(s) where the function $f(x)$ is monotonically decreasing.
(2) Translate the graph of the function $f(x)$ to the right by $\frac {π}{3}$ units and upwards by $\frac { \sqrt {3}}{2}$ units to obtain the graph of the function $g(x)$. Find the range of the function $g(x)$ when $x\in[0, \frac {π}{2}]$.

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