Be understanding of the venting.....It will go on for a long time (I have a friend whose H cheated about 5 years ago.....and even now she sometimes has to vent). Just kept listening, owning what is yours, and be patient. You did well today, but remember that it will keep happening.
I agree with you that actions are the right way to address a wrong. That said.....How your apology is received may depend on the other persons love language. Some people it may be flowers and others it may be a hug. You need to know what resonates with your wife's love language.
Now for Valentine's day...Give her flowers because you love her. Currently you haven't screwed up...so reinforce in her mind what she means to you.
