
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 line $m$ is perpendicular to plane $\alpha$, and line $n$ is in plane $\beta$, consider the following four propositions:
1. If $\alpha \parallel \beta$, then $m \perp n$.
2. If $\alpha \perp \beta$, then $m \parallel n$.
3. If $m \perp n$, then $\alpha \parallel \beta$.
4. If $m \parallel n$, then $\alpha \perp \beta$.

The sequence number(s) of the true proposition(s) is/are ____.

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