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human
How to understand that Godel's Incompleteness theorems and his Completeness theorem don't contradict each other?

As a layman, it seems that his Incompleteness theorems and completeness theorem seem to contradict each other, but it turns out they are both true.

The completeness theorem seems to say "anything true is provable." But the Incompleteness theorems seem to show that there are "limits to provability in formal axiomatic theories." 

I feel like I'm misinterpreting what these theorems say, and it turns out they don't contradict each other. Can someone help me understand why?
gpt
The completeness theorem says that any logical consequence of the axioms is provable. This means that we're not missing any logical rules, the ones we have are "complete". They suffice to prove everything you could hope to prove.

The incompleteness theorem says that any set of axioms is either self-contradictory, or cannot prove some true statement about numbers. You can still prove every logical consequence of the axioms you have, but you can never get enough axioms to ensure that every true statement about numbers is a logical consequence of them.

In a word: completeness says that every logical consequence of your axioms is provable, incompleteness says that there will always be true facts that are not a logical consequence of your axioms. (There are some qualifications you have to make when stating the incompleteness theorem precisely; the axioms are assumed to be computably listable, and so on.)