
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 $f(x)$ with domain $A$, if its range is also $A$, then the interval $A$ is called the invariant interval of $f(x)$. If the invariant interval of $g(x) = x + m + \ln x$ is $[e, +\infty)$, then the value of $m$ is ____.

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