Final answer:
Perform an emergent cricothyrotomy.
Step-by-step explanation:
The most appropriate next step in managing a 39-year-old man who is cyanotic, has insufficient respiratory effort, and has a difficultly fitting an oxygen facemask due to his full beard would be to perform an emergent cricothyrotomy. A cricothyrotomy involves making an incision through the skin and cricothyroid membrane to establish an airway. In this situation, where the patient is struggling to breathe and the usual oxygen delivery methods are not feasible, a cricothyrotomy is the fastest and most effective way to secure an airway.
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