
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 $f\left(x\right)=\frac{{x}^{2}}{1+{x}^{2}}$, if $f(\sqrt{1})=\frac{1}{2}$, $f(\sqrt{\frac{1}{2}})=\frac{1}{3}$, then find the value of $f(\sqrt{1})+f(\sqrt{2})+f(\sqrt{\frac{1}{2}})+f(\sqrt{3})+f(\sqrt{\frac{1}{3}})+…+f(\sqrt{n})+f(\sqrt{\frac{1}{n}})$

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