
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
Let $m$ and $n$ be two different lines, and $\alpha$, $\beta$, $\gamma$ be three different planes. Among the following statements, the correct ones are (write down the numbers of all correct statements):

1. If $m \parallel n$ and $n \parallel \alpha$, then $m \parallel \alpha$ or $m \subset \alpha$;
2. If $m \parallel \alpha$, $n \parallel \alpha$, $m \subset \beta$, and $n \subset \beta$, then $\alpha \parallel \beta$;
3. If $\alpha \perp \gamma$ and $\beta \perp \gamma$, then $\alpha \parallel \beta$;
4. If $\alpha \parallel \beta$, $\beta \parallel \gamma$, and $m \perp \alpha$, then $m \perp \gamma$.

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