
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 $f\left(x\right)=a\ln x-2x^{2}$, where $a$ is a real number. For any two distinct real numbers $p$ and $q$ in the interval $\left(0,1\right)$, the inequality $\frac{{f(p)-f(q)}}{{p-q}}＞1$ always holds. Find the range of real number $a$.

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