= Solution
\b[Either experiment is again possible.] The sequential experiment with $U=I$ repeats its first measurement outcome in every basis: the first <projective measurement> has prepared one of that basis's <eigenstates>, and the identity leaves it unchanged.
For the two-<qubit> experiment choose
$$
|\psi\rangle=|\Phi^+\rangle=\frac{|00\rangle+|11\rangle}{\sqrt2}
=\frac{|++\rangle+|--\rangle}{\sqrt2}.
$$
The two expansions exhibit identical outcomes in both specified bases. Each allowed equal-label record has <probability> $1/2$. These are fixed choices of $U$ and $|\psi\rangle$, respectively; neither depends on which of the two bases Alice selects.
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