The correct answer is principle, principal.

To determine the correct words for the blanks, we need to understand the difference between the homophones principle and principal:

1. Principle (noun): This word refers to a fundamental truth, rule, law, guideline, or belief. In the sentence, the phrase "many hands make light work" is a proverb or a fundamental rule of cooperation. Therefore, the first blank requires "principle" (i.e., "Going by the principle...").

2. Principal (noun/adjective): As a noun, this word refers to a person of high authority, most commonly the head of a school. In the sentence, the person who involved all the students in the task is the head of the school. Therefore, the second blank requires "principal" (i.e., "...the school principal involved all the students...").

Thus, the words that best fill the blanks are principle, principal.