
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
(1) Given that $\sqrt{a} + \frac{1}{\sqrt{a}} = 3$, find the value of $\frac{(a^2 + \frac{1}{a^2} + 3)}{4a + \frac{1}{4a}}$;
(2) Calculate $[(1 - \log_{6}3)^2 + \log_{6}2 \times \log_{6}18] \cdot \log_{4}6$.

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