
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 propositions. Indicate which of them are correct (fill in the serial number).
1. If line $m$ on plane $\alpha$ and line $n$ on plane $\beta$ are skew lines, and line $l$ is the intersection line of planes $\alpha$ and $\beta$, then $l$ intersects at most one of lines $m$ and $n$;
2. If line $m$ and line $n$ are skew, and line $n$ and line $l$ are skew, then line $m$ and line $l$ are skew;
3. There exists a plane $\gamma$ that is parallel to both skew lines $m$ and $n$.

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