
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:<br/>$(1)\frac{\sqrt{50}×\sqrt{32}}{\sqrt{8}}-4\sqrt{2}$;<br/>$(2)\sqrt{12}-6\sqrt{\frac{1}{3}}+\sqrt{48}$;<br/>$(3)(\sqrt{5}+3)(3-\sqrt{5})-(\sqrt{3}-1)^{2}$;<br/>$(4)(\sqrt{24}+\sqrt{50})÷\sqrt{2}-6\sqrt{\frac{1}{3}}$.

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