Dr$.$ Frank, following a messy divorce, has encountered significant financial difficulties. Dr$.$ Frank has a friend named Slick Slim who tells Dr$.$ Frank that he has been making lots of money by sell$-$ing people a wristband that allegedly places pressure on a nerve that signals hunger resulting in a lack of appetite. Slick Slim tells Dr$.$ Frank that, although the device does not really work, people who want to lose weight and look good in their bathing suits will do anything and that it sells like hotcakes. Slick Slim tells Dr$.$ Frank that he will pay Dr$.$ Frank $$500$ for every band that Dr$.$ Frank can sell to his patients. Dr$.$ Frank proceeds to mail letters to patients suggesting the use of the band for weight loss. He also uses the USPS to mail samples of the band to some patients along with letters encouraging purchase of the bands. Dr$.$ Frank then proceeds to bill Medicare for office consultations he has with patients when they come in to purchase the bands. The scheme is wildly successful. Dr$.$ Frank is able to entirely satisfy his alimony obligations within just a few months. Unfortunately, as patients begin to see that they are not having any weight loss, he has been receiving numerous complaints, and a friend of his told him that he could even be facing some criminal prosecution. Dr$.$ Frank is obviously involved in fraudulent activities.

Choose $2$ forms of fraudulent crimes that Dr$.$ Frank might be charged with and explain why they fit this scenario.

a$.$ Charge $1$: Based on what evidence

b$.$ Charge $2$: Based on what evidence