
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
For the function $y = f(x)$, if there exists an interval $[a, b]$ such that the range of values when $x \in [a, b]$ is $[ka, kb]$ ($k > 0$), then $y = f(x)$ is called a $k$-times value function. If $f(x) = \ln x + x$ is a $k$-times value function, then the range of values for the real number $k$ is ______.

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