
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
Compute the following expression:
$(1) ( \frac {1}{3})^{-1} - \log _{2}8 + (0.5^{-2} - 2) \times ( \frac {27}{8})^{ \frac {2}{3} }$;

(2) Given that $\sin \alpha + \cos \alpha = \frac {1}{5}$, where $0 < \alpha < \pi$, find the value of $\sin ^{2}\alpha - 2\sin \alpha \cos \alpha + 3\cos ^{2}\alpha$.

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