Nucleic Acids and Abiogenesis

In the 1950s, the scientists that were studying the origin of life felt sure they would solve the epic riddle within their lifetime. 50-odd years later, we've come to learn, they did not. And odds are, neither will we.
One of the leading theories supporting evolution is that of abiogenesis. That is, the idea that living things can come from nonliving things. Life had to begin somewhere.

In order for the first living organism to have developed, it would have needed nucleic acids. You probably remember them from your biological class; adenine, thymine, cytosine, guanine.

It is not commonly known that these nucleic acids have been found in nature, and have been synthesized in laboratories using naturally occurring processes and constituents.

Adenine has been created in a controlled laboratorty environment from hydrogen cyanide and ammonia. Both are naturally occurring, to some extent. It is not entirely impossible or even necessarily unlikely that these two chemicals were present on a primordial planet Earth.
Once adenine has been synthesized, the other nucleic acids can come from it.

In fact, adenine has been found in several meteorites, albeit in small concentrations. This leads one to wonder how much adenine could have been introduced to the planet via meteorites impacting the oceans of early Earth. It is safe to say that we can be quite sure that at least some adenine was present in the oceans--if not from (what some would deem coincidental) natural formations, from meteorites, or perhaps even other unconsidered sources.

Of course, something can't really be considered to be a living organism if it doesn't reproduce, or replicate. In order for the first living organism to have replicated, it would have needed more nucleic acids--but because of the extreme area of the oceans, the probably of it being able to collect the nucleic acids it needs to replicate would be very slim.

What if the organism was not in the ocean, but, rather, a small puddle? There would, hypothetically, probably be a much greater density of the required nucleic acids in a puddle than would be in the ocean.
Though, once the organism begins to replicate, the same problem arises--a lack of nucleic acids.

In order to solve both and either of these problems, it would be vital for the organism to be able to synthesize the nucleic acids for itself. The enzymes required could not have been existent after the organism began replicating, or the replication would not work. Strangely, the enzymes must have been present before life began, or during the originating of the first organism.
Every organism possesses the genes that allow for the encoding of the enzymes that make it possible for the organism to make its nucleic acids. You possess them, I possess them.
Assuming this, the genes responsible for allowing nucleic acid synthesis in an organism must have existed in the common ancestor of all living things in the world.

There are 11 enzymes necessary for synthesizing adenine in an organism. If any of them are missing or malfunctioning, adenine will not be synthesized.

This is a pretty extreme coincidence.

Can we dismiss the theories of abiogenesis on the grounds of irreducible complexity? Or can we continue to argue that we aren't even sure if we have the pieces of the puzzle, much less what the puzzle is supposed to look like when it's completed?