Begin a sentence with a verb sometimes. See, I just did. Twice.
As others have noted, you're apparently confusing gerunds with verbs in your example. But that said, gerunds are perfectly good words and can be used to vary your sentence structure.
I don't know where you were told that a sentence can never begin with a verb. Imperative sentences (i.e. commands) routinely start with verbs: "Go to the store." "Bring me the book." Etc. It's relatively rare otherwise in English, as the conventional structure is subject-verb-object, but it's not unheard of. "Thinking quickly, Bob leaped for the door." "'Leaving so soon?' Sally asked." Sometimes it's effective to use a non-standard word order for emphasis or to save an unexpected word for last. "Left in the middle of the night, he did." "Kill me they might, but they will never defeat me."
If you find that you are in a rut and all your sentences follow the same pattern, then, as Tylerharms says, I would definitely make an effort to consciously break the pattern. (Now that you mention this, I have to look at my own writing and see if I've fallen into this!) Of course one should avoid the opposite extreme, of trying so hard to vary your sentence constructions that you over-use odd phrasings.