The law does require employers to investigate harassment claims, and places upon the employee an obligation to investigate claims when they receive reasonable notice of a a complaint. Upon notice, the employer is obligated to take all reasonable steps necessary to halt any harassment.
“An employer whose sole action is to conclude that no harassment occurred cannot in any meaningful sense be said to have “remedied” what happened. Denial does not constitute a remedy.” Fuller v. City of Oakland (9th Cir. 1995) 47 F.3d 1522.
Please check the law of your state
Does "outside" mean "What extra", or that you think it too too long.
There is a heavy level of "reasonable" involved--"prompt" does not mean "before lunch", nor does it mean, "within three years."
For a very small employer to have an established "process" might be asking a bit much--but the complaint still needs to be investigated.