
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
 
Using $\overline{a b c}$ and $\overline{d e f g}$ to represent a three-digit number and a four-digit number respectively, where $a, b, c, d, e, f, g$ each represent different digits from 1 to 9. Given that $\overline{a b c} + $\overline{d e f g} = 2020$, find the difference between the maximum and minimum values of $\overline{a b c} \times \overline{d e f g}$.

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