
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
Define $||x||$ $(x\in R)$ as the integer closest to $x$. Let $F(x)=||x||$, for example, $F(\frac{4}{3})=1, F(\sqrt{2})=1$. Then, $\frac{1}{{F(1)}}+\frac{1}{{F(\sqrt{2})}}+\frac{1}{{F(\sqrt{3})}}+\frac{1}{{F(2)}}+…+\frac{1}{{F(\sqrt{99})}}+\frac{1}{{F(10)}}=\_\_\_\_\_\_$.

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