
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 three lines in space, a, b, c. The correct statements are numbered as follows:  
① If a⊥c and b⊥c, then a∥b;  
② If a∥b and b∥c, then a∥c;  
③ There is exactly one line that forms a 60° angle with line a through a point P in space;  
④ There are infinitely many lines that are perpendicular to two skew lines a and b.

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