
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 $l$, $m$, $n$ are distinct lines, and $\alpha$, $\beta$, $\gamma$ are distinct planes, consider the following four propositions:  
1. If $\alpha \parallel \beta$ and $l \subset \alpha$, then $l \parallel \beta$.  
2. If $\alpha \perp \gamma$ and $\beta \perp \gamma$, then $\alpha \perp \beta$.  
3. If $m \not\subset \alpha$, $n \subset \alpha$, and $m \parallel n$, then $m \parallel \alpha$.  
4. If $m \subset \alpha$, $n \subset \alpha$, $m \parallel \beta$, and $n \parallel \beta$, then $\alpha \parallel \beta$.  

Determine which of the above propositions are true. (Write down the numbers of all correct conclusions)

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