
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 the pairs of positive integers  $(m,n)$  such that the numbers  $A=n^2+2mn+3m^2+3n$ ,  $B=2n^2+3mn+m^2$ ,  $C=3n^2+mn+2m^2$  are consecutive in some order.

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