Both naproxen and Advil are pain relievers that, when taken in suffficient quantity, are also anti-inflammatories. Naproxen works more slowly but more steadily. Taking it twice a day keeps its anti-inflammatory action going (taken less, and it simply helps w/pain for the hours covered by the dose). Advil works more quickly, but requires a dose every four hours to reach anti-inflammatory levels.
For an acute situation of pain, we use Advil for a few days and then switch to naproxen. For longer-term chronic pain, naproxen is best, twice a day.
Using BOTH of these drugs could definitely cause gastric erosion, bleeding, and perhaps, as described in the nearby posts, leaking. I would only take ONE of them, and I would suggest that naproxen is gentler.
Also, you should know that Advil can cause major probelms with rebound pain, if used often. I believe naproxen itself can also cause rebound pain. Naproxen sodium, known as Aleve, doesn't cause any rebound, according to some research.
If you have any stomach problems, or more bruising than usual, that would be an indicator you should stop any of these drugs.
One of my kids does wears a medical device which has a cannula that is inserted every few days under her skin. Naproxen helped her pain a lot, but after a few weeks, the sites where the cannula was inserted would bleed and bruise excessively.
Now, if she has a period of bad pain and inflammation, such as bursitis (which she gets a lot from Lyme), we use Aleve twice a day for a couple of weeks, then stop. After a few weeks, she can repeat the Aleve for a couple of weeks, and so on.
In other words, naproxen and naproxen sodium are useful drugs. But doctors tend to say "take these twice a day" as a long-term regimen, which doesn't work for everyone, or maybe even for anyone. It is good to customize it to your individual needs and problems. But use what you can use safely to help your pain and inflammation.
And taking both naproxen and Advil is definitely excessive (and redundant).