
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 $k\in R$, the function $f(x)=\left\{{\begin{array}{l}{{e^x}-kx,x≥0,}\\{k{x^2}-x+1,x＜0．}\end{array}}\right.$. Four conclusions are given as follows:<br/>① When $k=1$, the function $f\left(x\right)$ has no zero points;<br/>② When $k \lt 0$, the function $f\left(x\right)$ has exactly one zero point;<br/>③ There exists a real number $k$ such that the function $f\left(x\right)$ has two zero points;<br/>④ There exists a real number $k$ such that the function $f\left(x\right)$ has three zero points.<br/>The correct conclusions are numbered as ______.

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