
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
Given the equation of a circle \( x^2 + y^2 = 4 \). Find points \( A(s, t) \) and \( B(m, n) \) on the coordinate plane such that the following two conditions are satisfied:
(1) The ratio of the distance from any point on the circle to point \( A \) and to point \( B \) is a constant \( k \);
(2) \( s > m \), \( t > n \), and \( m \) and \( n \) are natural numbers.

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