
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) If $a$ and $b$ are two skew lines, then there exists exactly one line that is perpendicular to both $a$ and $b$;
- (2) Two lines in space that do not have a common point are skew lines;
- (3) If $a$ and $b$ are two skew lines, then a line that intersects both $a$ and $b$ can be drawn through any point in space;
- (4) A line in a plane and a line outside the plane are skew lines;
- (5) Two lines located in two different planes are skew lines;
- (6) If line $a$ intersects line $b$, and line $b$ intersects line $c$, then line $a$ also intersects line $c$;
- (7) If $a$ and $b$ are skew lines, and $b$ and $c$ are skew lines, then $a$ and $c$ are also skew lines.  
Among these, the numbers of the incorrect propositions are ______.

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