= Solution
Use the first copy to determine computational-basis parity and the second to determine phase parity. On the first pair, Alice and Bob each measure the <Pauli operator> $Z$ and communicate their signs $z_A,z_B$. On the second, each measures $X$ in the $|+\rangle,|-\rangle$ basis and communicates the signs $x_A,x_B$.
Every <Bell state> is an eigenstate of both $Z\otimes Z$ and $X\otimes X$. Direct application to its two basis terms gives the table
$$
\begin{array}{c|cc}
\text{state}&z_Az_B&x_Ax_B\\\hline
\Phi^+&+1&+1\\
\Phi^-&+1&-1\\
\Psi^+&-1&+1\\
\Psi^-&-1&-1
\end{array}
$$
For example, $Z\otimes Z$ acts positively on $|00\rangle,|11\rangle$ and negatively on $|01\rangle,|10\rangle$; $X\otimes X$ exchanges the two terms in each pair, detecting their relative sign. Thus individual outcomes are random, but the products in the table are certain. The <Bell parity and phase observables> label the state uniquely.
\b[The two communicated parities identify all four states with probability one.] Each measurement is local and all remaining operations are classical, so the protocol is <LOCC discrimination of four Bell states using two copies>. Alice can simply send her two signs to Bob, who combines them with his own. Measuring $Z$ on the first copy destroys its phase information, but the second identical copy still supplies it; this is why the two-copy assumption enables this protocol.
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