
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
A function $f(x)$ satisfies the following conditions: ① $f(x)$ is a monotonically increasing function on the interval $\left[a,b\right]$; ② The range of $f(x)$ on $\left[a,b\right]$ is $\left[ka,kb\right]$. The interval $\left[a,b\right]$ is called a $k$-level "harmonic interval" of $y=f(x)$. If the function $f(x)=x^{2}-2x+4$ has a $k$-level "harmonic interval", then the range of $k$ is ______.

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