
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 $$f(x)=2\sin x\cos x+2\sqrt{3}\cos^2 x-\sqrt{3}.$$  
(1) If the range of the function on $$[m, \frac{\pi}{2}]$$ is $$[-\sqrt{3}, 2]$$, find the minimum value of $m$;  
(2) In triangle ABC, $$f\left(\frac{A}{4}\right)=2$$, $$\sin B=\frac{3\sqrt{3}}{4}\cos C$$, find $\sin C$.

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