
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
Regular tetrahedron \( ABCD \) is projected onto a plane sending \( A, B, C, \) and \( D \) to \( A', B', C', \) and \( D' \) respectively. Suppose \( A'B'C'D' \) is a convex quadrilateral with \( A'B' = A'D' \) and \( C'B' = C'D' \), and suppose that the area of \( A'B'C'D' = 4 \). Given these conditions, the set of possible lengths of \( AB \) consists of all real numbers in the interval \([a, b)\). Compute \( b \).

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