
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 $a$ is a non-zero constant:
1. Find the intervals of monotonicity for $f(x)$ when $a=1$.
2. Let $b \in \mathbb{R}$. If $f(x) \leq b - a$ for all $x > 0$, find the minimum value of $\frac{b}{a}$.

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