
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 two distinct lines $l$ and $m$, and two distinct planes $\alpha$ and $\beta$, consider the following propositions:

1. If $l \subset \alpha$, $m \subset \alpha$, $l \parallel \beta$, and $m \parallel \beta$, then $\alpha \parallel \beta$.

2. If $l \subset \alpha$, $l \parallel \beta$, and $\alpha \cap \beta = m$, then $l \parallel m$.

3. If $\alpha \parallel \beta$ and $l \parallel \alpha$ , then $l \parallel \beta$.

4. If $l \perp \alpha$, $m \parallel l$, and $\alpha \parallel \beta$, then $m \perp \beta$.

Identify all the true propositions.

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