In reflex action, brain do play any role. reflex action is controlled by spinal cord.

Reflex actions are sudden involuntary responses which does not involve thinking. For example, when we touch a hot object, we withdraw our hand immediately without thinking. The sensory nerves that detect the heat are connected to the nerves that move the muscles of the hand. Such a connection of detecting the signal from the nerves and responding to it quickly is known as reflex arc. Reflex arcs are formed in the spinal cord and the information reaches the brain and brain responses to it.