
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 pairs of natural numbers \( x, y \in [1 ; 8] \) that satisfy the equation

\[ \sqrt{xx, xxx \ldots} = y, yyy \ldots \]

(The decimal representation of each of the numbers \( xx, xxx \ldots \) and \( y, yyy \ldots \) consists of an infinite number of identical digits.)

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