
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 lines $m$, $n$ and planes $\alpha$, $\beta$, consider the following three propositions: 
1. If $m \parallel \alpha$ and $n \parallel \alpha$, then $m \parallel n$;
2. If $m \parallel \alpha$ and $n \perp \alpha$, then $n \perp m$;
3. If $m \perp \alpha$ and $m \parallel \beta$, then $\alpha \perp \beta$.

The correct propositions are numbered as follows.

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