
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 triangle $\bigtriangleup DEF$ where its vertices lie on the parabola $y = x^2 - 4x + 4$, point $D$ is at the vertex of the parabola, and $\overline{EF}$ is parallel to the x-axis, calculate the length of $\overline{EF}$ if the area of $\bigtriangleup DEF$ is $32$.

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