improvise
v.v. to create or perform something without preparing it first. You use this when you have to make a plan or a speech at the last minute.
v. to compose, perform, or deliver without prior preparation; to produce something using whatever materials are available at the moment.
I forgot my notes, so I had to improvise the speech.
When the power went out during the dinner party, we had to improvise and eat by candlelight.
The jazz musicians began to improvise over the basic chord progression, creating a complex and spontaneous melody that captivated the entire audience.
From French improviser; ultimately from Latin improvisus.
Can be used transitively (to improvise a solution) or intransitively (to improvise during a performance).