
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
Read the following material and then answer the following questions: When simplifying algebraic expressions, sometimes we encounter expressions like $\frac{5}{\sqrt{3}},\frac{2}{\sqrt{3}+1}$, which can be further simplified as follows: <br/>① $\frac{5}{\sqrt{3}}=\frac{5×\sqrt{3}}{\sqrt{3}×\sqrt{3}}=\frac{5\sqrt{3}}{3}$; ② $\frac{2}{\sqrt{3}+1}=\frac{2(\sqrt{3}-1)}{(\sqrt{3}+1)(\sqrt{3}-1)}=\sqrt{3}-1$; <br/> The method of simplification mentioned above is called rationalizing the denominator. <br/> $(1)$ Simplify: $\frac{2}{\sqrt{5}-\sqrt{3}}$; <br/> $(2) \frac{1}{\sqrt{4}+\sqrt{2}}+\frac{1}{\sqrt{6}+\sqrt{4}}+\frac{1}{\sqrt{8}+\sqrt{6}}+\ldots +\frac{1}{\sqrt{2018}-\sqrt{2016}}+\frac{1}{\sqrt{2020}+\sqrt{2018}}+\frac{1}{\sqrt{2022}+\sqrt{2020}$.

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