It should say הטוב כי לא כלו טובך והמרחם כי לא תמו רחמיך - It seems non-sequiter [whatever that means...:-)] to say that He is טוב so He keeps doing רחמים and that He has רחמים so He keeps doing chesed.
This Leil Shabbos after davening a friend asked me the same question. On Shabbos morning I chanced upon a sefer that cited the explanation of Rav Itzele Blazer [prized talmid of Rav Yisroel of Salant].
Tov is when someone deserves it. Rachamim is when he doesn't deserve it but is a rachmanus case and needs it. הטוב כי לא כלו רחמיך - Hashem is Tov and gives us when we are deserving but ALSO gives us when we are not deserving and need extra mercy.
Chesed is when a person is not a rachmanus case but would enjoy the kindness [e.g. a stranger has enoough food to fill himself up but is invited to a family for a sumptuous meal. That is not rachmanus but chesed]. והמרחם כי לא תמו חסדיך - Hashem is not only giving when we need rachmanus [e.g. a sick or poor person] but even when we just need chesed, His chesed never ends [e.g. making a successful business deal when we already have enough money to live for the next few months].
We should be zocheh to see Hashem's Tov, Rachamim and Chesed.
לזכות ר' משה גבריאל בן יהודית לברכה והצלחה בכל מעשי ידיו!
