To call something absurd is to point out its utter senselessness or foolishness. To call something incongruous is to point that it is out of place or inconsistent. These two adjectives, which emphasize slightly different qualities, overlap when the incongruity or inconsistency under discussion is so pronounced or outlandish that it veers into the absurd or laughable.
When you determine something, you conclude or ascertain it by reasoning or observation. When you verify something, you prove its truth or correctness, or you confirm it. There is a resoluteness to both terms, but verify has veritas (truth) at its core. To verify the accuracy of information, as a journalist does, is to fact-check it or confirm that it’s true. To verify the authenticity of an antique or artwork is to confirm its provenance or history of ownership. And to verify the identity of someone, as when accessing sensitive information online, is to make certain that that person is who they claim to be.
The adjective innovative emphasizes the introduction of something new. It is similar to the adjective creative insofar as it deals with originality, but innovative is far less likely to describe artistic endeavors, such as painting or writing. It is more at home in the world of technology and business-oriented problem solving, likely influenced by commercially oriented uses of the noun innovation to refer to new products introduced on the market, or the act of introducing new products.