Reimbursing Business Travel Purchased with Mileage Rewards for Tax Filing

I recently went on a business trip and used mileage rewards from my personal airline mileage account to purchase my airfare, which was significantly cheaper than buying the ticket in cash. I transferred these rewards to my airline account from my credit card points, which my credit card company allows me to use as a method of deducting my credit card balance. Since the trip was for business purposes, I'm wondering if it's possible to reimburse myself for the airfare from my LLC, using a conversion rate of 1 mile to 1 cent, similar to the credit card company's value method. I want to make sure I can claim this as a business expense on my tax filing. Has anyone else been in a similar situation or have experience with this kind of reimbursement? I appreciate any advice or guidance on how to proceed.