
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 \(C: x^2=4y\) intersects with the line \(y=kx+a\) (where \(a>0\)) at two points, M and N.  
(1) When \(k=0\), determine the equations for the tangents to curve C at points M and N.  
(2) Is there a point P on the y-axis such that for varying values of \(k\), \(\angle OPM\) always equals \(\angle OPN\)? Give a reasoning for your answer.

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