
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 planes $\alpha, \beta$, and line $m, n$, the following propositions are given:

$\text{(1)}$ If $m \parallel \alpha, n \parallel \beta, m \parallel n$, then $\alpha \parallel \beta$

$\text{(2)}$ If $\alpha \parallel \beta, m \parallel \alpha, n \parallel \beta$, then $m \parallel n$

$\text{(3)}$ If $m \perp \alpha, n \perp \beta, m \perp n$, then $\alpha \perp \beta$

$\text{(4)}$ If $\alpha \perp \beta, m \perp \alpha, n \perp \beta$, then $m \perp n$

Identify the true proposition(s).

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