
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, its focus is F, and E is a point on the positive semi-axis of y. OE=3OF (O is the origin of the coordinate), and there is a point M(x₀, y₀) on the parabola C, where x₀≠0, such that the tangent line l passing through point M is perpendicular to ME. The intercept of the tangent line l on the y-axis is _____.

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