
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 expressions:
1. $\lg 8 + \lg 125 - \left(\frac{1}{7}\right)^{-2} + 16^{\frac{3}{4}} + (\sqrt{3} - 1)^0$
2. Given that $\tan \alpha = 3$, find the value of $\frac{2\sin \alpha - \cos \alpha}{\sin \alpha + 3\cos \alpha}$.

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