
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 $f(x)= \begin{cases} x\sin x, & 0 < x < \pi \\ \sqrt {x}, & x\geqslant \pi\end{cases}$, $g(x)=f(x)-kx(k\in\mathbb{R})$  
(1) When $k=1$, the function $g(x)$ has \_\_\_\_\_\_ zero points;  
(2) If the function $g(x)$ has three zero points, then the range of $k$ is \_\_\_\_\_\_.

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