
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
In the Cartesian coordinate system $xOy$, the curve C: $x^2=6y$ intersects with the line l: $y=kx+3$ at points M and N.
(1) When $1<k<2$, find the range of values for the area of triangle MON.
(2) Does there exist a point P on the y-axis such that, as k varies, angle POM is always equal to angle PON? If so, find the equation of the circle with line segment OP as its diameter. If not, explain why.

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