
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 $f(x)=2\sqrt{3}\sin{x}\cos{x}-\cos{2x}$, where $x\in\mathbb{R}$. Find:<br/>
$(1)$ The smallest positive period of the function $f(x)$;<br/>
$(2)$ Let $α\in\left(0,\frac{\pi}{3}\right)$, and $f(α)=\frac{6}{5}$. Find the value of $\sin{2α}$.

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