
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) $3 \sqrt{20} - \sqrt{45} - \sqrt{\frac{1}{5}}$  
(2) $\frac{\sqrt{6} \times \sqrt{3}}{\sqrt{2}} - 1$  
(3) $\sqrt{16} + 327 - 2 \cdot \sqrt{\frac{1}{4}}$  
(4) $(\sqrt{3} - \sqrt{5})(\sqrt{5} + \sqrt{3}) - (\sqrt{5} - \sqrt{3})^2.$

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