
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
For any $x_1, x_2$ ($x_1 \neq x_2$) in the domain of the function $f(x) = \ln x$, the following conclusions are made:  
① $f(x_1 + x_2) = f(x_1) \cdot f(x_2)$;  
② $f(x_1 \cdot x_2) = f(x_1) + f(x_2)$;  
③ $$\frac{f(x_{1}) - f(x_{2})}{x_{1} - x_{2}} > 0$$  
Among the above conclusions, the correct one(s) is(are) __________.

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