
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 the following expressions:

(1) $4 \sqrt{54} \times 3 \sqrt{2} \div (-\frac{3}{2} \sqrt{\frac{1}{3}})$

(2) $(3 + \sqrt{5})(3 - \sqrt{5}) - (\sqrt{3} - 1)^2$

(3) $- \sqrt{32} - \frac{1}{2} \sqrt{75} + 2 \sqrt{0.5} - 3 \sqrt{\frac{1}{27}}$

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