
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 the function \( f(x) = \ln x - ax \), where \( a > 0 \), and \( g(x) = f(x) + f^{\prime}(x) \):

1. If the maximum value of the function \( f(x) \) in the interval \( 1 \leq x \leq e \) is -4, find the expression for the function \( f(x) \).
2. Find the range of values for \( a \) such that the function \( g(x) \) is monotonic on the interval \( (0, +\infty) \).

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