
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) $\lg 8 + \lg 125 - \left( \frac{1}{7} \right)^{-2} + 16^{\frac{3}{4}} + \left( \sqrt{3} - 1 \right)^{0}$  
(2) Given $\tan\alpha = 3$, 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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