
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 natural pairs  $ (x,y)$ , such that  $ x$  and  $ y$  are relative prime and satisfy equality:  $ 2x^2 \plus{} 5xy \plus{} 3y^2 \equal{} 41x \plus{} 62y \plus{} 21$ .

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