
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
Consider the following four propositions:
① If a line is perpendicular to two lines within a plane, then the line is perpendicular to that plane.
② If a line is perpendicular to every line in a plane, then the line is perpendicular to that plane.
③ If line $l$ is parallel to plane $\alpha$, and line $m$ is parallel to plane $\alpha$, then $l$ is parallel to $m$.
④ If line $a$ is parallel to line $b$, and line $l$ is perpendicular to $a$, then $l$ is perpendicular to $b$.
Identify the correct propositions.

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