
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 a function $f(x)$ defined on $\left[0,+\infty \right)$, for any $x_{1}$, $x_{2}\in \left[0,+\infty \right)$ with $x_{1}\neq x_{2}$, we have $\frac{{f({{x_2}})-f({{x_1}})}}{{{x_2}-{x_1}}}＞2$, and $f\left(1\right)=2020$. Determine the range of values of $x$ that satisfy the inequality $f\left(x-2021\right) \gt 2\left(x-1012\right)$.

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