The Beatles released "Day Tripper" in December of 1965. As you can see by the picture, "We Can Work It Out" was the B-side(!). The concept and riff were Lennon's, while Paul helped with the verses, making it a true Lennon-McCartney song (one of the few).
In this video, another promotional film, Lennon and McCartney look as if they're connected at the hip. John and Paul did, after all, audition for a gig in Reading, England, as "The Nurk Twins" while still attending school in Liverpool. You can really see how well King Features Syndicate captured the essence of each Beatle for the cartoon, based on how they look in this "film".
The Nurk Twins