
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
For any $x_{1}$, $x_{2} \in \left[1,+\infty \right)$, when $x_{2} \gt x_{1}$, the inequality $a\ln\frac{x_{2}}{x_{1}}-2(x_{2}-x_{1})＜0$ holds. Find the range of real number $a$.

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