
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 $m$ and $n$ are different lines, and $\alpha$ and $\beta$ are non-coincident planes. Proposition $p$: If $\alpha \parallel \beta$, $m \subset \alpha$, $n \subset \beta$ then $m \parallel n$; Proposition $q$: If $m \perp \alpha$, $n \perp \beta$, $m \parallel n$, then $\alpha \parallel \beta$. Among the following propositions, the true ones are:

1. "p or q" is true;
2. "p and q" is true;
3. p is true and q is false;
4. "$\neg p$" is true.

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