Oddly, you have to actually assert that right in many jurisdictions. In the US, say something like “I plead the fifth” or “I choose to remain silent” and assert your right to an attorney, and shut up until the attorney comes and only speak at the discretion of the attorney. Just staying silent opens you up to attempted manipulation, whereas they must provide an attorney if requested and the attorney may have options to strike some of the manipulation while you wait for the attorney.

Our right to shut the fuck up is almost as important as the 1st right. We should use it more often.