
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 that $m$ and $n$ are two different lines in space, and $\alpha$ and $\beta$ are two different planes in space, determine the correct propositions among the following:
  1. If $m \parallel \alpha$ and $m \parallel \beta$, then $\alpha \parallel \beta$.
  2. If $m \perp \alpha$ and $m \parallel \beta$, then $\alpha \perp \beta$.
  3. If $m \parallel \alpha$ and $m \parallel n$, then $n \parallel \alpha$.
  4. If $m \perp \alpha$ and $\alpha \parallel \beta$, then $m \perp \beta$.

The correct proposition numbers are $\boxed{\text{answer}}$.

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