Offer received. Currently employed. How to proceed with negotiations?

Currently employed. Great place. No complaints aside from lower salary in comparison to similar companies.

Applied to some jobs to test the waters. Got an offer, but the job isn’t the most ideal. I’d love to use this to negotiate a higher salary in my current position. I don’t want to screw my current or potential employers over. Want to do this with the proper cadence.

Do I accept the offer, and simply begin negotiations with my current company? It’s been years since I’ve applied for jobs. Any insight is appreciated!

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