A country with a history of high inflation is considering two different strategies to achieve long-term price stability.

Strategy A involves joining a large monetary union, adopting its common currency, and handing over control of monetary policy to the union's highly respected central bank.

Strategy B involves passing a law that makes its own national central bank politically independent and gives it a single, overriding legal mandate to maintain a low and stable rate of inflation.

Explain the fundamental mechanism by which each of these different strategies is intended to work, and identify the key principle they both share in their approach to controlling inflation.