
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 expressions $1+ \frac{1}{2^{2}} < \frac{3}{2}, 1+ \frac{1}{2^{2}}+ \frac{1}{3^{2}} < \frac{5}{3}$, $1+ \frac{1}{2^{2}}+ \frac{1}{3^{2}}+ \frac{1}{4^{2}} < \frac{7}{4}...$, we can induce that $1+ \frac{1}{2^{2}}+ \frac{1}{3^{2}}+...+ \frac{1}{(n+1)^{2}} < $ \_\_\_\_\_\_.

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