
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
Among the following four propositions, the incorrect ones are \_\_\_\_\_\_.
① If lines $a$ and $b$ form equal angles with plane $\alpha$, then $a \parallel b$;
② If two lines $a \parallel b$ and line $a \parallel$ plane $\alpha$, then $b$ must be parallel to plane $\alpha$;
③ If a line and a slant line in plane $\alpha$ have perpendicular projections within plane $\alpha$, then they must be perpendicular to each other;
④ If two points $A$, $B$ are at equal distances from plane $\alpha$, then line $AB \parallel$ plane $\alpha$.

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