
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 that $P$ is any point on the line $y=-1$, and two tangents are drawn from point $P$ to the parabola $x^2=4y$, with the points of tangency being $A$ and $B$. The lines $PA$ and $PB$ intersect the $x$-axis at points $E$ and $F$ respectively, and $O$ is the origin. Calculate the ratio of the area of $\triangle PEF$ to the area of $\triangle OAB$.

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