
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 $f(x)=\log_{a}(x^{2}-2ax)$ where $a > 0$ and $a\neq 1$, it is known that for any $x_{1}$ and $x_{2}$ within $[3,4]$ and $x_{1}\neq x_{2}$, the inequality $\frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}} > 0$ holds true. Determine the range of values for the real number $a$.

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