
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
Observe the following expressions:  
$(\sqrt{2}+1)(\sqrt{2}-1)=1$,  
$(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})=1$,  
$(\sqrt{4}+\sqrt{3})(\sqrt{4}-\sqrt{3})=1$,  
$\ldots \ldots $  
Based on the pattern presented above, calculate:  
$\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}+\frac{1}{\sqrt{4}+\sqrt{3}}+\cdots+\frac{1}{\sqrt{99}+\sqrt{100}}$.

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