
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 the function $f(x)=\begin{cases} & \dfrac{1}{2}\sqrt{x^{2}+1},x\geqslant 0, \\ & -\ln (1-x),x < 0, \\ \end{cases}$ if the function $F(x)=f(x)-kx$ has exactly two zeros, then the range of $k$ is \_\_\_\_\_\_\_\_.

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