
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 $x_1$ and $x_2$ ($x_1 \neq x_2$) in the domain of the function $f(x)$, the following properties hold:
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. $\frac{f(x_1)-f(x_2)}{x_1-x_2} > 0$;
4. $f\left(\frac{x_1+x_2}{2}\right) < \frac{f(x_1)+f(x_2)}{2}$.

Determine the correct statements when $f(x) = \log x$.

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