
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 the following four propositions about distinct lines $m$, $n$, $l$, and a plane:

1. If $m \subset \alpha$, $l \cap \alpha = A$, and $A \notin m$, then $l$ and $m$ are not coplanar.
2. If $l$ and $m$ are skew lines, $l \parallel \alpha$, $m \parallel \alpha$, and $n \perp l$, $n \perp m$, then $n \perp \alpha$.
3. If $l \subset \alpha$, $m \subset \alpha$, $l \cap m = A$, $l \parallel \beta$, $m \parallel \beta$, then $\alpha \parallel \beta$.
4. If $l \parallel \alpha$, $m \parallel \beta$, $\alpha \parallel \beta$, then $l \parallel m$.

The false proposition(s) is/are.

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