Step 1: Meaning of the phrase.
The phrase "at a snail's pace" refers to moving or happening very slowly, just like how a snail moves at a slow speed.
Step 2: Analysis of the options.
Very intelligent refers to someone with high intellect.
Very alert refers to someone who is keenly aware of their surroundings.
Very slowly refers to a slow movement, which matches the phrase "at a snail's pace."
Very fast refers to quick movement, which is the opposite of the phrase.
Step 3: Conclusion.
Thus, the correct answer is very slowly.
Final Answer:
\[
\boxed{\text{Very slowly is the correct answer.}}
\]