
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
If $P$ is any point outside of two skew lines $l$ and $m$, then the false proposition among the following statements is __________ (fill in the number).
1. There is exactly one line passing through point $P$ that is parallel to both $l$ and $m$;
2. There is exactly one line passing through point $P$ that is perpendicular to both $l$ and $m$;
3. There is exactly one line passing through point $P$ that intersects both $l$ and $m$;
4. There is exactly one line passing through point $P$ that is skew to both $l$ and $m$.

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