
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:  
(1) If line $a$ is parallel to line $b$, and line $a$ is parallel to plane $\alpha$, then line $b$ is parallel to plane $\alpha$.  
(2) If line $a$ is parallel to plane $\alpha$, and line $b$ is contained in plane $\alpha$, then plane $\alpha$ is parallel to line $b$.  
(3) If line $a$ is parallel to plane $\alpha$, then line $a$ is parallel to all lines within plane $\alpha$.  
(4) If line $a$ is parallel to plane $\alpha$, and line $a$ is parallel to line $b$, and line $b$ is not contained in plane $\alpha$, then line $b$ is parallel to plane $\alpha$.  
The correct proposition(s) is/are __________.

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