
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
(Experimental class assignment)  
(1) Given $\sin \alpha - \sin \beta = -\frac{1}{3}$ and $\cos \alpha - \cos \beta = \frac{1}{2}$, find $\cos (\alpha - \beta) =$ ______. (Write out the calculation process)  
(2) In $\triangle ABC$, given that $\tan A$ and $\tan B$ are the two real roots of the equation $3x^2 - 7x + 2 = 0$, find $\tan C$?

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