
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 circle C is $x^2+y^2=r^2$, and a fixed point M$(x, y)$, the line $l: xx+yy=r^2$ has the following two sets of assertions:  
Set I & Set II  
(a) Point M is inside circle C and M is not the center (1) Line $l$ is tangent to circle C  
(b) Point M is on circle C (2) Line $l$ intersects circle C  
(c) Point M is outside circle C (3) Line $l$ does not intersect circle C  
Using assertions from Set I as conditions and assertions from Set II as conclusions, write all possible valid propositions in the form of p⇒q.

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