
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 $f(x) = \sin x (\cos x - \sqrt{3} \sin x)$.

1. Find the smallest positive period of the function $f(x)$.
2. The graph of the function $y = \sin 2x$ is translated $a (0 < a < \frac{\pi}{2})$ units to the left and $b$ units downwards to obtain the graph of the function $y = f(x)$. Find the value of $ab$.
3. Find the range of the function $f(x)$ on the interval $[0, \frac{\pi}{2}]$.

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