
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
In plane $\alpha$, there is an equilateral triangle $A'BC$. A line $DE$ is parallel to $BC$ and intersects $A'B$ at $D$ and $A'C$ at $E$. Triangle $A'DE$ is folded along $DE$ to make it perpendicular to plane $\alpha$, resulting in triangle $ADE$. When is $AB$ the shortest, considering the placement of line $DE$ that is parallel to $BC$?

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