Hot pot in sink

I accidentally put a boiling hot dairy pot (which was not used for dairy within 24 hours ) with eggs in it directing into my stainless steel meat sink and let it sit there.
Do I need to kasher the pot or the sink as in this case I did use the sink with something directly from fire ?

You said -

“ I did use the sink with something directly from fire”

Was that something a meat pot, or a meat sauce, or the like , - in other words, what was it the you say made the sink used for meat?

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Well the sink is considered a meat sink because in the past , boiling hot pots of let’s say chicken soup were placed directly in the sink.
No hot meat or hot meat in a hot pot were placed in this sink within 24 hours of the incident with the dairy pot with eggs .
The “something “ used in the case described in my post was eggs in a boiling hot dairy pot which was not used for dairy in the last 24 hours