
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
The graph of the function $y=\sin x \cos x$ is translated two units down and to the left along the line $y=\sqrt{3}x$, resulting in the function $y=f(x)$. Determine the analytical expression for $f(x)$.

A) $y=2\sin(2x+2)-\sqrt{3}$
B) $y=2\sin(2x+1)-\sqrt{3}$
C) $y=\frac{1}{2}\sin(2x+2)-\sqrt{3}$
D) $y=\frac{1}{2}\sin(2x+1)-\sqrt{3}$

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