Explanation:

Alright, let's break this down:

- The original sentence: "The teacher advised the children to not went near the lake."

- That's grammatically off—"to not went" doesn't work.

Now, the options:

1. don't go

- This is the imperative form ("Don't go near the lake"). It's fine as a direct order but doesn't fit after "advised the children to...".

2. No improvement

- Not a chance. The original is incorrect.

3. not to go

- This is the right fit. After "advised," the structure is "to" + base form of the verb. So, "advised the children not to go near the lake" is spot-on.

4. not to be going

- That's continuous tense, which isn't needed here. It's awkward and unnecessary for a general warning.

So the best choice is option 3: "not to go."