
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
Let $a$, $b$, and $c$ be three lines in space. The following four propositions are given:  
① If $a \perp b$ and $b \perp c$, then $a \parallel c$;  
② If $a$ and $b$ are skew lines, and $b$ and $c$ are skew lines, then $a$ and $c$ are also skew lines;  
③ If $a$ and $b$ intersect, and $b$ and $c$ intersect, then $a$ and $c$ also intersect;  
④ If $a$ and $b$ are coplanar, and $b$ and $c$ are coplanar, then $a$ and $c$ are also coplanar.  
The number of true propositions is     .

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