As you grow older, an injury to your ______ may take longer to ______.

To choose the correct words for this sentence, we need to distinguish between the homophones heel and heal:
1. Heel (noun) refers to the back part of the foot below the ankle.
2. Heal (verb) means to mend, repair, or become healthy again after an injury.

Applying these definitions to the context of the sentence:
- The first blank requires a noun representing a body part: "an injury to your heel".
- The second blank requires a verb representing the recovery process: "may take longer to heal".

Therefore, the correct sequence is heel/heal.