"Thank you very much" is actually a cliche for people who wants to show that they are grateful to someone.
Are there any related forms or verbs that can be used in formal way instead of "Thank you!"?
I don't think "thank you very much" is a cliché. You could use it to express polite gratitude in a formal setting and as long as your tone was sincere, nobody would mind.
In most situations, a good way to show sincerity (if you're concerned that your phrasing sounds cliché or automatic) is to be specific. "Thank you" is all well and good, but "thank you for your thoughtful gift" is even better. "Thank you very much for taking the time to help me" erases any doubt that you are being insincere or thoughtless because you are specifying exactly what you feel grateful for.
The key as pointed out by Abby is to be specific. Any form of "thank you" can seem generic, but thanking them specifically for what they did for you shows you were thinking about them and the situation when you wrote it. Additionally, explaining what their help enabled you to do, what you did, and the results of that is even better! This is the difference between:
They are both specific about what they helped you with, but the second one is better because it demonstrates what you actually did with their help. What they helped you achieve.