
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
Consider the following four propositions regarding distinct lines $m$, $n$, $l$, and planes $\alpha$, $\beta$:
1. If line $m$ is contained in plane $\alpha$, line $l$ intersects plane $\alpha$ at point $A$, and point $A$ is not on line $m$, then line $l$ and line $m$ are not coplanar.
2. If lines $l$ and $m$ are skew lines, line $l$ is parallel to plane $\alpha$, line $m$ is parallel to plane $\alpha$, and line $n$ is perpendicular to both lines $l$ and $m$, then line $n$ is perpendicular to plane $\alpha$.
3. If line $l$ is contained in plane $\alpha$, line $m$ is contained in plane $\alpha$, line $l$ intersects line $m$ at point $A$, line $l$ is parallel to plane $\beta$, and line $m$ is parallel to plane $\beta$, then plane $\alpha$ is parallel to plane $\beta$.
4. If line $l$ is parallel to plane $\alpha$, line $m$ is parallel to plane $\beta$, and plane $\alpha$ is parallel to plane $\beta$, then line $l$ is parallel to line $m$.

The correct propositions are (fill in the serial numbers).

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