
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
We consider the set of four-digit positive integers  $x =\overline{abcd}$  with digits different than zero and pairwise different. We also consider the integers  $y = \overline{dcba}$  and we suppose that  $x > y$ . Find the greatest and the lowest value of the difference  $x-y$ , as well as the corresponding four-digit integers  $x,y$  for which these values are obtained.

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