
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 distinct lines $a$, $b$, $c$, and a plane $\gamma$, consider the following propositions:

1. If $a\parallel b$ and $b\parallel c$, then $a\parallel c$;
2. If $a\perp b$ and $b\perp c$, then $a\perp c$;
3. If $a\parallel \gamma$ and $b\parallel \gamma$, then $a\parallel b$;
4. If $a\perp \gamma$ and $b\perp \gamma$, then $a\parallel b$;
5. If $a\perp b$ and $b\parallel c$, then $a\perp c$;
6. If $a\parallel b\parallel c$, then $a$, $b$, $c$ are coplanar.

Identify the true propositions from the list above.

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