
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 $f(x)=\lg x$, for any $x_1$, $x_2$ ($x_1 \neq x_2$) in the domain of function $f(x)$, the following conclusions are drawn:

1. $0 < f′(3) < f(3)-f(2) < f′(2)$;
2. $0 < f′(3) < f′(2) < f(3)-f(2)$;
3. $\dfrac{f(x_1)-f(x_2)}{x_1-x_2} > 0$;
4. $f\left( \dfrac{x_1+x_2}{2}\right) < \dfrac{f(x_1)+f(x_2)}{2}$.

Among the above conclusions, the correct ones are.

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