
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 point P(-1, 4) and the circle C: $(x-2)^2+(y-3)^2=1$. Determine which of the following statements are correct:

① Point P is inside circle C.
② A line l passing through point P bisects circle C. If so, the equation of line l is $x+3y-11=0$.
③ A line l passing through point P is tangent to circle C. If so, the equation of line l is $y-4=0$ or $3x+4y-13=0$.
④ A ray of light starting from point P reflects off the x-axis and reaches circle C with the minimum distance being $\sqrt{58}$.

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