
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
As shown, given the tetrahedron \(ABCD\) where \(AB \perp BC\), \(BC \perp CD\), and \(CD \perp AB\):

1. Identify the face that is perpendicular to the face \(BCD\) and provide proof.
2. If \(AB = BC = 1\) and \(CD = x\), and the dihedral angle \(C-AD-B\) has a plane angle \(\alpha\) such that \(\sin \alpha = f(x)\), find the expression for \(f(x)\) and the range of values for \(\alpha\).

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