
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 $f(x)=-4\cos ^{2}x+4 \sqrt {3}a\sin x\cos x+2$. If the graph of $f(x)$ is symmetric with respect to the point $(\frac{\pi}{12},0)$,

(1) Find the real number $a$ and the interval(s) where $f(x)$ is decreasing;

(2) Find the smallest positive period of $f(x)$ and the range of $f(x)$ on the interval $[-\frac{\pi}{4}, \frac{\pi}{6}]$.

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