
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
In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. Given that the point $(a, b)$ lies on the line $x(\sin A - \sin B) + y \sin B = c \sin C$.
(1) Find the measure of angle $C$;
(2) If $\triangle ABC$ is an acute triangle and satisfies $\frac{m}{\tan C} = \frac{1}{\tan A} + \frac{1}{\tan B}$, find the minimum value of the real number $m$.

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