
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:<br/>$(1)\sqrt{50}+\sqrt{32}-\sqrt{2}$;<br/>$(2)\sqrt{{{(3)}^2}}+\sqrt[3]{{-8}}-|1-\sqrt{2}|$;<br/>$(3)(\sqrt{5}-1)^{2}-(\sqrt{6}-\sqrt{5})(\sqrt{6}+\sqrt{5})$;<br/>$(4)\frac{{\sqrt{8}+\sqrt{18}}}{{\sqrt{2}}}+(\sqrt{24}-\sqrt{\frac{1}{6}})÷\sqrt{3}$.

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