
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
Let the function $f(x)=x^{2}-x\ln x+2$, if there exists an interval $[a,b]\subseteq \left[\frac{1}{2},+\infty\right)$, such that the range of $f(x)$ on $[a,b]$ is $[k(a+2),k(b+2)]$, then the range of $k$ is \_\_\_\_\_\_\_\_\_\_\_\_.

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