Reach out is being used inappropriately these days. It differs from contacting a person. Reach out has the connotation of making an overture. It suggests a sort of tentativeness in the act of initiating a possible contact. That sense of tentativeness is not present in the rather neutral contact.
Reaching out implies that the other person has to reach out as well. Contact does not imply that. The other person may well choose not to reciprocate the gesture. Recall the situation in which a person extends his or her hand when introduced to someone, and that person just stands there rudely without taking the proffered hand and shaking it. Reaching out is a gesture of goodwill. Contact is not necessarily so. One can contact another person in order to express anger or insult that person. But when one reaches out the intentions are always positive and honorable.
Consider the following passage from Whispers of the Heart by J. Allen Wilson
Therefore, this is all the more reason that we should reach out
from our hearts daily to those that surround us, reach out and
lift up one another. We must extend our hand in peace,....
So it is better to use reach me instead of reach out.