
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 $f(x)=2\sin \frac {x}{2}\cos \frac {x}{2}-2 \sqrt {3}\sin ^{2} \frac {x}{2}+ \sqrt {3}$.
(1) Find the interval(s) where the function $f(x)$ is monotonically decreasing.
(2) Given that $\alpha \in (\frac {\pi}{6}, \frac {2\pi}{3})$, and $f(\alpha)= \frac {6}{5}$, find the value of $f(\alpha- \frac {\pi}{6})$.

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