
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 a line is drawn through point P(2,-1) to be tangent to the parabola x^2 = 4y at points A and B, the tangents PA and PB intersect the x-axis at points E and F, respectively. Let O be the origin of the coordinate system. Find the ratio of the area of ∆PEF to the area of ∆OAB.

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