The sentence you provided is in the present participle tense.
How to explain
The action described, "stumbling to the kitchen" and "reaches deep into one of the cabinets," are in the present tense, indicating an action currently happening or ongoing.
The present participle tense denotes an ongoing action, formed by adding "-ing" to the base verb (e.g., walking, eating).
The verb "reaches" is in the simple present tense, signifying an action carried out at the present moment. This tense choice gives a sense of immediacy and ongoing activity to the action described, capturing the moment as it unfolds in the narrative.