
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 propositions:
       ① In space, if two lines are both parallel to a third line, then these two lines are parallel;
② In space, if two lines are both perpendicular to a third line, then these two lines are parallel;
③ In space, if two lines are both parallel to a plane, then these two lines are parallel;
④ In space, if two lines are both perpendicular to a plane, then these two lines are parallel;
Among these, the correct propositions are numbered as ______. (Write down the numbers of all correct propositions)

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