
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
If \(2 \sin (3x) = a \cos (3x + c)\), find all values of \(ac\). In the choices below, \(k\) runs through all integers.

(a) \(-\frac{\pi}{2}\)  
(b) \(2k\pi\)  
(c) \(-\pi\)  
(d) \((4k - 1)\pi\)

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