
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 There is exactly one line through a point outside a given line that is parallel to the given line;
② There is exactly one line through a point that is perpendicular to a given plane;
③ There is exactly one line through a point on a plane that is parallel to the given plane;
④ There is exactly one plane through a point that is perpendicular to a given line;
⑤ There is exactly one plane through a point outside a given plane that is parallel to the given plane.  
Among these propositions, the correct ones are (write down the numbers of all correct propositions).

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