
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 that points M(1, 4) and N(3, 2) lie on circle C, and the line $2x - 3y + 6 = 0$ is an axis of symmetry for circle C.
(1) Find the equation of the line that passes through the point (5, 1) and is tangent to circle C.
(2) If a line l passes through point P(1, 0) and intersects circle C such that the midpoint of the chord is A, and it intersects line m: $x + 2y + 2 = 0$ at point B, determine whether |PA|•|PB| is a constant value. If it is, find the constant; if not, provide an explanation.

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