
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]


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In the regular quadrangular pyramid V-ABCD (with the base being a square and all lateral edges being equal), AB=2, VA=$$\sqrt{6}$$, and the pyramid can rotate around AB at will. During the rotation, if CD is parallel to plane α, find the range of the area of the orthogonal projection of the regular quadrangular pyramid V-ABCD on plane α.

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