
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 that $\tan \alpha = -2$, calculate the value of $\dfrac {3\sin \alpha + 2\cos \alpha}{5\cos \alpha - \sin \alpha}$.
(2) Given that $\sin \alpha = \dfrac {2\sqrt{5}}{5}$, calculate the value of $\tan (\alpha + \pi) + \dfrac {\sin \left( \dfrac {5\pi}{2} + \alpha \right)}{\cos \left( \dfrac {5\pi}{2} - \alpha \right)}$.

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