
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given the following conditions (where $l$ and $a$ are lines, and $\alpha$ is a plane):
① $l$ is perpendicular to three lines within $\alpha$, which are not parallel to each other;
② $l$ is perpendicular to countless lines within $\alpha$;
③ $l$ is perpendicular to three sides of a regular hexagon within $\alpha$;
④ $a$ is perpendicular to $\alpha$, and $l$ is perpendicular to $a$.
Among these, the conditions that are sufficient for "$l$ is perpendicular to $\alpha$" are numbered as follows.

Present the answer in LaTex format: \boxed{Your answer}
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