In a manner that shows extreme self-centeredness or obsession with oneself; in the way an egomaniac would behave.
From egomaniacal plus the adverb-forming suffix -ly. This transforms the adjective into an adverb describing how an action is performed with egomaniacal tendencies.
Egomaniacally is the adverb form—so while an egomaniac IS obsessed, they act egomaniacally, which means every action is filtered through their self-obsession, like they can't help but make everything about themselves.
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