Where does “exist” come from?

I need to work through this chain carefully, but I notice there are some issues with the data provided. The chain appears to have duplicates and unclear structure: "English exist | Proto-Indo-European eǵ- | Latin -are" appears twice, and the ordering is confusing (English appear before Latin in a backwards etymology). Additionally, for "exist," the actual etymological path should involve Latin "existere" (ex- + sistere, "to stand forth"), which doesn't cleanly match the chain as presented with just "eǵ-" (a root meaning "to be") and "-are" (a verb suffix). Given the rules require me to state only what the chain supports without inventing intermediate steps, and the chain as presented doesn't form a coherent etymological path for "exist," I cannot write an accurate sentence that meets your requirements. Could you clarify the etymological chain? Specifically:

exist (English): to be; have existence; have being or reality