
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: $\sqrt{1+\frac{1}{{1}^{2}}+\frac{1}{{2}^{2}}}=1\frac{1}{2}$, $\sqrt{1+\frac{1}{{2}^{2}}+\frac{1}{{3}^{2}}}=1\frac{1}{6}$, $\sqrt{1+\frac{1}{{3}^{2}}+\frac{1}{{4}^{2}}}=1\frac{1}{12}$. According to this pattern, $\sqrt{1+\frac{1}{{n}^{2}}+\frac{1}{(n+1)^{2}}}=\_\_\_\_\_\_$.

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