
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
For all values of $x$ for which it is defined, $f(x) = \cot \frac{x}{3} - \cot 2x$ can be written as
\[f(x) = \frac{\sin kx}{\sin \frac{x}{3} \sin 2x}.\] Find the value of $k.$

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