
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:
1) $\sqrt{12}+\sqrt{20}-2\sqrt{3}+\sqrt{5}$;
2) $(\sqrt{8}+\sqrt{\frac{1}{2}})\times \sqrt{2}-(\sqrt{3}+1)(\sqrt{3}-1)$;
3) Simplify first, then find the value: $(\frac{x}{x-1}-1)÷\frac{{x}^{2}+2x+1}{{x}^{2}-1}$, where $x=\sqrt{2}-1$.

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