
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]


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$a$, $b$, and $c$ are three non-intersecting lines in space. Here are five propositions:
   $(①)$ If $a \parallel b$, $b \parallel c$, then $a \parallel c$;
   $(②)$ If $a \perp b$, $b \perp c$, then $a \parallel c$;
   $(③)$ If $a$ intersects with $b$, and $b$ intersects with $c$, then $a$ intersects with $c$;
   $(④)$ If $a$ is in plane $\alpha$, and $b$ is in plane $\beta$, then $a$ and $b$ are definitely skew lines;

The correct proposition(s) is/are _______ (only fill in the number(s)).

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