
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 $a$ and $b$ be two lines, and $\alpha$ and $\beta$ be two planes. There are four propositions below:  
(1) If the angles formed by $a$, $b$ with $\alpha$ are equal, then $a \parallel b$;  
(2) If $a \parallel \alpha$, $b \parallel \beta$, and $\alpha \parallel \beta$, then $a \parallel b$;  
(3) If $a \subset \alpha$, $b \subset \beta$, and $a \parallel b$, then $\alpha \parallel \beta$;  
(4) If $a \perp \alpha$, $b \perp \beta$, and $\alpha \perp \beta$, then $a \perp b$. Among these, the true propositions are     . (Write down the numbers of all true propositions)

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