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

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