
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 $\alpha$ and $\beta$ be two different planes. Consider the following propositions:  
(1) If $\alpha \parallel \beta$, $m \subset \beta$, $n \subset \alpha$, then $m \parallel n$;  
(2) If $\alpha \parallel \beta$, $m \perp \beta$, $n \parallel \alpha$, then $m \perp n$;  
(3) If $\alpha \perp \beta$, $m \perp \alpha$, $n \parallel \beta$, then $m \parallel n$;  
(4) If $\alpha \perp \beta$, $m \perp \alpha$, $n \perp \beta$, then $m \perp n$.  
Among the above propositions, the numbers of all true propositions are.

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