Using classification of previous sample in neural networks
The approach you describe is predicting base on the features of the current step and the previous states.
If you believe that there is information on the previous states, than i would try to approach this problem in the Time Series approach.  

The algorithms in this approach basically do what you request for, they predict based on the features of the current step and based on the previous states.
You can learn about the approach to understand it better in this cs231n video.  

You can also look for tutorials on implementing models that fit the time-series problem.
The most popular model i know is caleld LSTM.
Here is a tutorial on implementing LSTM in keras.

I hope you will find it these helpful.
If you have any more questions or you would like more guidance, just let me know :)