= Solution
Alice performs a projective <Bell-basis measurement> on her qubits $C$ and $A$. Outcome $(x,z)$ occurs with probability $1/4$ and leaves Bob's qubit in
$$
X^xZ^z|\alpha\rangle.
$$
Alice sends the two classical bits $(x,z)$ to Bob. He applies the inverse Pauli operation
$$
(X^xZ^z)^{-1}=Z^zX^x,
$$
recovering $|\alpha\rangle$ exactly, up to an irrelevant <global phase>. This is <quantum teleportation>: only <local operations and classical communication> are used, while the shared Bell pair supplies the entanglement resource.
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