A baby is learning to walk with the assistance of its living room couch. The baby starts at the couch and at each given time the baby will make a decision. It will either take a brave step forward, stand in place not knowing what to do, or fearfully take a step back towards the couch with probabilities $0.2$, $0.5$, and $0.3$ respectively. The baby will never go behind the couch (so when at the couch the baby has probability $0.2$ of moving forward and probability $0.8$ of staying at the couch).

If you were to observe this baby for an extremely long amount of time, what proportion of the time would the baby be at the couch?