
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 a function $f_{K}(x)$ whose domain is the set of real numbers $R$, and it satisfies $f_{K}(x)= \begin{cases} 1, & x\in K \\ 0, & x\notin K \end{cases}$ (where $K$ is a non-empty proper subset of $R$), if there are two non-empty proper subsets $M$, $N$ of $R$, and $M\cap N=\varnothing$, then the range of $F(x)= \dfrac {f_{M}(x)+f_{N}(x)+1}{f_{M\cup N}(x)+1}$ is \_\_\_\_\_\_.

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