
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
a) Two positive integers are chosen. The sum is revealed to logician  $A$ , and the sum of squares is revealed to logician  $B$ . Both  $A$  and  $B$   are given this information and the information contained in this sentence. The conversation between  $A$  and  $B$  goes as follows:  $B$  starts 

B: ` I can't tell what they are.' 
A: ` I can't tell what they are.'
B: ` I can't tell what they are.'
A: ` I can't tell what they are.' 
B: ` I can't tell what they are.'
A: ` I can't tell what they are.'
B: ` Now I can tell what they are.'

What are the two numbers? 

b) When  $B$  first says that he cannot tell what the two numbers are,  $A$  receives a large amount of information. But when  $A$  first says that he cannot tell what the two numbers are,  $B$  already knows that  $A$  cannot tell what the two numbers are. What good does it do  $B$  to listen to  $A$ ?

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