
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 four propositions:

① If two lines within a plane are parallel to another plane, then the two planes are parallel to each other;

② If a plane passes through a perpendicular line of another plane, then the two planes are perpendicular to each other;

③ Two lines that are perpendicular to the same line are parallel to each other;

④ If two planes are perpendicular, then a line within one of the planes that is not perpendicular to their line of intersection is also not perpendicular to the other plane.

Among these, the true propositions are __________ (write down the numbers of all correct propositions).

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