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

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