
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) $2 \sqrt{3} \times \sqrt[3]{1.5} \times \sqrt[6]{12}$

(2) $\lg \frac{3}{7} + \lg 70 - \lg 3 - \sqrt{(\lg 3)^{2} - \lg 9 + 1}$

(3) Given $\tan \alpha = 2$, find the value of $4\sin^{2}\alpha - 3\sin \alpha \cos \alpha - 5\cos^{2}\alpha$.

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