How does the speaker support his idea that his soul has grown deep like the river

I bathed in the Euphrates when dawns were young.

I built my hut near the Congo and it lulled me to sleep.

I looked upon the Nile and raised the pyramids above it.

I heard the singing of the Mississippi when Abe Lincoln went down to New Orleans,

and I've seen its muddy bosom turn all golden in the sunset.