My wife (67) goes up steep hills amazingly well. She puts her mountain or hybrid in the combination giving her the most cadence and just spins her way up. Takes her forever, but she does it.

Incidentally, you stated

"When I'm on the big ring and spin, I feel like I'm going nowhere and get frustrated."

I assume you meant the small chain ring and not the big chain ring. If you are in the big chain ring, no wonder you can't do it. Try the small chain ring in front and the largest cassette in the rear. Then make changes from there by choosing a larger cassette as you can.

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