I have a sentence which includes a quote of a multi-line poem. I'm wondering what's the correct way to express it in HTML.

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Example

Yesterday the poem

Would it be ok if I took some of your time?
Would it be ok if I wrote you a rhyme?

kept bouncing in my head.

I believe this whole example should live in a <p> tag, since it wouldn't make sense to split "Yesterday the poem" or "kept bouncing in my head." away from the rest: they're not valid independently. The whole example together is one sentence.

For a poem represented this way I would normally use a <blockquote>. However you can't nest a blockquote inside a p, thus I need to change something.

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What's the semantically correct way to represent my sentence?