
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
Given the sequence \(\{a_{n}\}\) with the general term formula \(a_{n}=\frac{1}{(n+1) \sqrt{n}+n \sqrt{n+1}}\) for \(n \in \mathbb{N}^{*}\), determine how many rational terms are there among the terms \(S_{1}, S_{2}, \cdots, S_{2008}\).

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