
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, let $g(x) = \cot \frac{x}{3} - \cot x$. This function can be expressed as
\[ g(x) = \frac{\sin mx}{\sin \frac{x}{3} \sin x}.\]
Find the value of $m$.

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