
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
(1) Given $\cos \beta =-\dfrac{3}{5}$, and $\beta$ is an angle in the second quadrant, find the value of $\sin \beta$.

(2) Given $\dfrac{\tan \alpha }{\tan \alpha -6}=-1,$ find the value of $\dfrac{2\cos \alpha -3\sin \alpha }{3\cos \alpha +4\sin \alpha }$.

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