
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 $f(x)=\log_a(x^2-2ax)$ ($a > 0$ and $a \neq 1$) satisfies that for any $x_1, x_2 \in [3,4]$ and $x_1 \neq x_2$, the inequality $\frac{f(x_1)-f(x_2)}{x_1-x_2} > 0$ holds, then the range of the real number $a$ is.

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