
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 square \(ABCD\), \(AB = 2\). Point \(E\) is the midpoint of \(AB\), and \(F\) is a point on side \(BC\) such that \(BF = x\). To fold triangles \(\triangle AED\) and \(\triangle DCF\) such that \(A\) and \(C\) coincide at point \(A'\), forming a tetrahedron \(A' - EFD\), what are the possible values for \(x\)?

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