
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
Determine all the pairs  $(a,b)$  of positive integers, such that all the following three conditions are satisfied:
1-  $b>a$  and  $b-a$  is a prime number
2- The last digit of the number  $a+b$  is  $3$ 3- The number  $ab$  is a square of an integer.

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