
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
Determine the value of $\frac{1}{2^{2}{-}1}{+}\frac{1}{3^{2}{-}1}{+}\frac{1}{4^{2}{-}1}{+…+}\frac{1}{(n{+}1)^{2}{-}1}$. The options are:
A) $\frac{n{+}1}{2(n{+}2)}$
B) $\frac{3}{4}{-}\frac{n{+}1}{2(n{+}2)}$
C) $\frac{3}{4}{-}\frac{1}{2}(\frac{1}{n{+}1}{+}\frac{1}{n{+}2})$
D) $\frac{3}{2}{-}\frac{1}{n{+}1}{-}\frac{1}{n{+}2}$

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