
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 $f(x) = \ln x + ax$.

(1) If the tangent line to the function $f(x)$ at $x=1$ is $y = 2x + m$, find the values of the real numbers $a$ and $m$.

(2) If the function $f(x)$ has two different zeros $x_1$, $x_2$ within its domain, determine the range of the real number $a$.

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