What's the difference between "agradezco" and "gracias"?

Question

What's the difference between "agradezco" (from the verb 'agradecer') and "gracias"? Both mean "Thank you" but when would you use one over the other? Please explain making reference to the below examples:

Example 1:

Gracias por su gentileza. _{(Thanks, that’s nice of you)}

Example 2:

Gracias, es muy fácil. Voy mañana con mi familia. _{(Thanks, that’s very easy. I’m going tomorrow with my family.)}

Example 3:

Te agradezco mucho la invitación, pero… _{Thanks very much the invitation, but…}

Example 4:

Le agradezco mucho. _{Thank you very much}

Example 5:

Muchas gracias. _{Thank you very much}

Answer 1

As you say, "agradecer" is a verb, whereas "gracias" is just a noun used as an idiom itself.

You use "gracias" in the same way you use "thank you".

On the other hand, "Le agradezco que..." means kind of I am grateful that.... You can also use estoy agradecido, which would be a more literal translation of "I'm grateful".