F-111 bombers flying from carriers ?

Remember the famous World War 2 raid when those B-24 bombers were
placed on the USS Hornet and sent to bomb Japan ?

I just got done reading that in 1965 the United States landed C-130
Herculees planes on a US aircraft carrier.

So that got me thinking. I'm not a Navy man or Air Force man, so this
question may sound crazy to some of you, but please at least address
it.

Let's talk hypothetically here. What if, at some point late in the
cold war the United States decided to stage a " Doolittle " type raid
on some country by having a small number of F-111 bombers take off
from a giant Nimitz class carrier. Could it have been done ?

Remember the 1986 raid on Libya ? Our F-111 bombers had to fly about
4,000 miles from their bases in Great Britain.

Or would the F-111 have been too big ? I'm not talking about storing
the planes below the carrier deck, or about having them return to the
carrier and land on it.

But would it have been possible to have a special mission and have
F-111's take off from a carrier ?