Your LLC likely doesn't own that vehicle. That still would be your Personal vehicle, and you are using it for personal and business Mileage.
That means the business never tracks Mileage for a vehicle it doesn't own, nor does it pay operating expenses for the vehicle.
You track mileage as a Personal vehicle with mixed use.
This is why Mileage Rates are used, and are considered an allowance and not a real expense.
Now that you have this LLC, you should ask your own CPA or tax preparer if you can submit for Mileage Reimbursement under an accountable plan.