
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 solution process: $\frac{1}{\sqrt{5} + \sqrt{4}} = \frac{1}{\sqrt{5} + \sqrt{4}} \times \frac{(\sqrt{5} + \sqrt{4})(\sqrt{5} - \sqrt{4})}{(\sqrt{5} + \sqrt{4})(\sqrt{5} - \sqrt{4})} = \frac{\sqrt{5} - \sqrt{4}}{1}, \frac{1}{\sqrt{6} + \sqrt{5}} = \frac{1}{\sqrt{6} + \sqrt{5}} \times \frac{(\sqrt{6} + \sqrt{5})(\sqrt{6} - \sqrt{5})}{(\sqrt{6} + \sqrt{5})(\sqrt{6} - \sqrt{5})} = \frac{\sqrt{6} - \sqrt{5}}{1}$, please answer the following questions:

(1) Based on the solution process above, please write out $\frac{1}{\sqrt{2} + 1} = \_\_\_; \frac{1}{n + 1} + \frac{1}{\sqrt{n} + \sqrt{n-1}} = \_\_\_$;

(2) Using the method above, simplify: $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \cdots + \frac{1}{\sqrt{98} + \sqrt{99}} + \frac{1}{\sqrt{99} + \sqrt{100}}.$

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