
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 parabola C: x²=4y with a focus at point F, and the line y=kx+m (m>0) intersecting the parabola C at two distinct points M and N.
(1) If the tangent lines to the parabola C at points M and N are perpendicular, find the value of m.
(2) If m=2, find the minimum value of |MF|•|NF|.

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