Generally yes — Aleve (naproxen) and Tylenol (acetaminophen) are different kinds of pain reliever, and the NHS says it's OK to take them together for short periods, but stick to each label's dosing and check with your pharmacist.
Naproxen is an NSAID and acetaminophen is a separate, non-NSAID pain reliever, so they don't duplicate the same drug or the same main risk — which is why the NHS states it's OK to take naproxen with over-the-counter paracetamol (acetaminophen) for short periods. The combination to avoid is naproxen with ibuprofen, aspirin, or any other NSAID, because doubling up NSAIDs raises the risk of stomach bleeding and ulcers; MedlinePlus warns naproxen alone can already cause ulcers, bleeding, or holes in the stomach or intestine. Because acetaminophen is not an NSAID, it can be added for extra pain relief without piling on the same NSAID stomach and heart risks. This is not a promise of safety for everyone — it depends on your dose, how long you use it, and your health.
Keep each drug within its own limit: do not exceed the Aleve/naproxen package directions (over-the-counter, typically every 8–12 hours), and stay under the acetaminophen daily maximum on the Tylenol label — check every product, since cold/flu and combination medicines often hide extra acetaminophen and you can overdose by stacking them. Use the combination only for a few days; if you regularly need both or need them beyond a few days, talk to your doctor. Never add ibuprofen, aspirin, or another NSAID on top of naproxen. Be extra cautious or ask a clinician first if you have stomach ulcers or GI bleeding history, kidney or liver disease, heart disease or a prior heart attack/stroke, drink alcohol heavily, or take blood thinners (e.g. warfarin), steroids (e.g. prednisolone), or SSRIs/SNRIs, or are pregnant. Stop and seek care for black/tarry stools, vomiting blood, severe stomach pain, or signs of a heart attack or stroke.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.