
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 four propositions, the correct one is ___________

(1) If $a\parallel b$ and $b\parallel c$, then $a\parallel c$.

(2) If $a\perp b$ and $b\perp c$, then $a\parallel c$.

(3) If $a\parallel \alpha$ and $b\subset \alpha$, then $a\parallel b$.

(4) If $a\parallel b$ and $b\parallel \alpha$, then $a\parallel \alpha$.

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