
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 a function y = f(x), if there exists an interval [a, b] such that when x ∈ [a, b], the range of f(x) is [ka, kb] (k > 0), then y = f(x) is called a k-value function. If f(x) = lnx + x is a k-value function, then the range of the real number k is \_\_\_\_\_\_.

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