
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
How many distinct positive integers can be expressed in the form  $ABCD - DCBA$ , where  $ABCD$  and  $DCBA$  are 4-digit positive integers?  (Here  $A$ ,  $B$ ,  $C$  and  $D$  are digits, possibly equal.)
Clarification:   $A$  and  $D$  can't be zero (because otherwise  $ABCD$  or  $DCBA$  wouldn't be a true 4-digit integer).  

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