
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
$(1)$ Simplify:①$\frac{1}{{\sqrt{2}}}=\_\_\_\_\_\_.$ ②$\frac{1}{{\sqrt{3}-1}}=\_\_\_\_\_\_.$<br/>$(2)$ Calculate: $\frac{1}{{2-\sqrt{3}}}-\frac{2}{{\sqrt{3}-1}}$.<br/>$(3)$ Calculate: $\frac{1}{{1+\sqrt{2}}}+\frac{1}{{\sqrt{2}+\sqrt{3}}}+\frac{1}{{\sqrt{3}+\sqrt{4}}}+\ldots +\frac{1}{{\sqrt{2018}+\sqrt{2019}}}$.

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