
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
The sequence \(\left\{a_{n}\right\}\) is defined by \(a_{1}=1.5\) and \(a_{n}=\frac{1}{n^{2}-1}\) for \(n \in \mathbb{N}, n>1\). Are there any values of \(n\) such that the sum of the first \(n\) terms of this sequence differs from 2.25 by less than 0.01? If yes, find the smallest such value of \(n\).

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