
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 $a \in \mathbb{R}$,
(1) Determine the intervals on which the function $f$ is monotonic.
(2) When $a < 0$, find the minimum value of $f(x)$ on the interval $[1, 2]$.

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