
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
Among the following statements:  
(1) Corresponding angles are equal;  
(2) There is only one line through a point that is perpendicular to a given line;  
(3) The angle bisectors of two adjacent angles formed by the intersection of two lines are perpendicular to each other;  
(4) If three lines intersect pairwise, there are always three intersection points;  
(5) If $a\parallel b$ and $b\parallel c$, then $a\parallel c$;  
(6) If $a\perp b$ and $b\perp c$, then $a\perp c$.  
The correct statements are __________.

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