I can understand your confusion! I have double digit songs on my playlist titled "Fate" and it happens to be the prefix for a very prominent anime series. It did not occur to me that "fate" was on the image. The song comes from the OP song's LP, "Fate" is the A-side, "Omoi" is the B-side. The anime itself is called "Break Blade" in Japan or "Broken Blade" in the west.
"Fate" is the OP. Unfortunately, "Omoi" is not featured in the anime itself. Kokia also did the ED for the 6th and final episode (hour long episodes).