
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 lines $l, m$ and planes $\alpha, \beta$, identify the correct propositions from the following statements:
1. If $\alpha \parallel \beta$ and $l \subset \alpha$, then $l \parallel \beta$;
2. If $\alpha \parallel \beta$ and $l \perp \alpha$, then $l \perp \beta$;
3. If $l \parallel \alpha$ and $m \subset \alpha$, then $l \parallel m$;
4. If $\alpha \perp \beta$, $\alpha \cap \beta = l$, $m \subset \alpha$, and $m \perp l$, then $m \perp \beta$.

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