
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 Two lines parallel to the same plane are parallel;

② Two lines perpendicular to the same plane are parallel;

③ If a line is parallel to a plane, then it is parallel to any line within that plane;

④ If a line is perpendicular to a plane, then it is perpendicular to any line within that plane.

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

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