
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 $f(x)=\log_{a}(x^{2}-ax+3)$ ($a > 0$ and $a \neq 1$) satisfies that for any $x_{1}, x_{2}$, when $x_{1} < x_{2} \leqslant \frac{a}{2}$, then $f(x_{1})-f(x_{2}) > 0$, determine the range of the real number $a$.

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