
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 ellipse \(\Gamma: \frac{x^{2}}{4}+y^{2}=1\), point \(P(1,0)\), lines \(l_{1}: x=-2, l_{2}: x=2\), chords \(AB\) and \(CD\) of the ellipse \(\Gamma\) pass through point \(P\), and line \(l_{CD}\): \(x=1\). The lines \(AC\) and \(BD\) intersect \(l_{2}\) and \(l_{1}\) at points \(E\) and \(F\) respectively. Find the ratio of the y-coordinates of points \(E\) and \(F\).

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