
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
Observation and discovery: $\frac{1}{\sqrt{2}+1}=\frac{\sqrt{2}-1}{(\sqrt{2}+1)(\sqrt{2}-1)}=\frac{\sqrt{2}-1}{(\sqrt{2})^{2}-1}=\frac{\sqrt{2}-1}{2-1}=\sqrt{2}-1$; $\frac{1}{\sqrt{3}+\sqrt{2}}=\frac{\sqrt{3}-\sqrt{2}}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})}=\frac{\sqrt{3}-\sqrt{2}{(\sqrt{3})^{2}-(\sqrt{2})^{2}}=\frac{\sqrt{3}-\sqrt{2}}{3-2}=\sqrt{3}-\sqrt{2}$...<br />(1) Simplify: $\frac{1}{\sqrt{11}+\sqrt{10}}$;<br />(2) Write directly: $\frac{1}{\sqrt{n+1}+\sqrt{n}}$=______;<br />(3) Evaluate: $\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}+\frac{1}{\sqrt{4}+\sqrt{3}}+…+\frac{1}{\sqrt{100}+\sqrt{99}}$.

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