Final answer:
Barnaby is in the sensorimotor stage of cognitive development because his action of checking for toys under the blanket shows he understands object permanence.
Step-by-step explanation:
The stage of cognitive development at which Barnaby operates when he pulls a blanket outside to check if his toys are still there is the sensorimotor stage. Within this stage, particularly between 5 and 8 months old, children develop the concept of object permanence, which refers to the understanding that objects continue to exist even when they cannot be seen or heard. Barnaby's action of pulling the blanket to find out if the toys are still there demonstrates his grasp of object permanence, solidifying that he is within the sensorimotor stage of cognitive development.