
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
Calculate:
(1) $\left( \frac {1}{3} \right)^{-1} - \log_{2}8 + \left(0.5^{-2} - 2\right) \times \left( \frac {27}{8} \right)^{ \frac {2}{3}}$
(2) Given $\tan\alpha = -2$, compute the value of $\frac {\sin(\pi + \alpha) + 2\sin\left( \frac {\pi}{2} - \alpha \right)}{\sin(-\alpha ) + \cos(\pi - \alpha)}$.

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