That's strange that a carpool lane is at the far right. Was there a solid white line that prohibits you from getting out of that lane for a distance? Anyway, I would contest it and try to plead my case in traffic court. The fines are pretty steep for carpool violations so it's worth it. I would suggest taking pictures and maybe even getting a fairly detailed map of that area.

At worst you waste some time but this sounds worth fighting.

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