
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) If $\alpha$ is an angle in the third quadrant and $\sin \alpha =-\dfrac{5}{13}$, find $\tan \dfrac{\alpha }{2}$;  
(2) If $\tan \alpha=2$, find the value of ${{\sin }^{2}}(\pi -\alpha )+2\sin (\dfrac{3\pi }{2}+\alpha )\cos (\dfrac{\pi }{2}+\alpha )$.

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