
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 a circle passes through points A(2, -3) and B(-2, -5), and the center C of the circle is on the line $l: x-2y-3=0$,
(1) Find the standard equation of this circle;
(2) Determine the positional relationship between points $M_1(0, 1)$, $M_2(2, -5)$, and the circle.

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