
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
Find all positive integers  $A,B$  satisfying the following properties:
(i)  $A$  and  $B$  has same digit in decimal. 
(ii)  $2\cdot A\cdot B=\overline{AB}$  (Here  $\cdot$  denotes multiplication,  $\overline{AB}$  denotes we write  $A$  and  $B$  in turn. For example, if  $A=12,B=34$ , then  $\overline{AB}=1234$ )

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