
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 two distinct lines $a$ and $b$, and three distinct planes $α$, $β$, and $γ$, consider the following statements:

$①$ If $a$ is parallel to $b$ and $b$ is a subset of $α$, then $a$ is parallel to $α$.

$②$ If $a$ is parallel to $b$ and $a$ is parallel to $α$, then $b$ is parallel to $α$.

$③$ If the intersection of $α$ and $β$ is $a$, $b$ is a subset of $γ$, $b$ is parallel to $β$, and $a$ is a subset of $γ$, then $a$ is parallel to $b$.

Determine the correct statement(s) number(s).

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