
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
Simplify the following expressions:
(1) $$\left(\frac{1}{4}\right)^{-2} + \left(\frac{1}{6\sqrt{6}}\right)^{-\frac{1}{3}} + \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} + \frac{1}{2} \cdot 1.03^0 \cdot (-\sqrt{6})^3$$
(2) $$(\lg 2)^2 + \lg 20 \times \lg 5 + \log_9 2 \cdot \log_4 3.$$

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