
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 line $a$, line $b$, and plane $\alpha$, which of the following propositions is correct? Fill in the blank with the serial number.  
① If $a \parallel b$, $b \subset \alpha$, then $a \parallel \alpha$;  
② If $a \parallel b$, $a \parallel \alpha$, then $b \parallel \alpha$;  
③ If $a \parallel \alpha$, $b \subset \alpha$, then $a \parallel b$;  
④ If $a \perp \alpha$, $b \perp \alpha$, then $a \parallel b$.

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