
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
Let  $\overline{abcd}$  be one of the 9999 numbers  $0001, 0002, 0003, \ldots, 9998, 9999$ . Let  $\overline{abcd}$  be an *special* number if  $ab-cd$  and  $ab+cd$  are perfect squares,  $ab-cd$  divides  $ab+cd$  and also  $ab+cd$  divides  $abcd$ . For example 2016 is special. Find all the  $\overline{abcd}$  special numbers.**Note:** If  $\overline{abcd}=0206$ , then  $ab=02$  and  $cd=06$ .

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