
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
As shown in the diagram, \(ABCD\) is a rectangle with \(AB = 8\) and \(BC = 4\). \(M\) and \(N\) are the midpoints of \(AB\) and \(CD\), respectively. A dynamic line \(l\) serves as the folding crease, such that after each fold, point \(M\) lands on edge \(CD\) at point \(M'\). From \(M'\), draw \(M'P\) perpendicular to \(CD\) and intersecting line \(l\) at point \(P\). The trajectory of point \(P\) forms curve \(E\).

1. Establish an appropriate coordinate system and find the equation of curve \(E\).
2. Point \(F\) lies on \(MN\) with \(\overrightarrow{FN} = -3 \overrightarrow{FM}\). A line passing through point \(F\) intersects curve \(E\) at points \(S\) and \(T\), such that \(\overrightarrow{SF} = \lambda \overrightarrow{FT}\). Find the range of the real number \(\lambda\).

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