
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 among the following statements, the false one is __________. (Fill in the serial number)

① There is exactly one line through point $P$ that is parallel to both $l$ and $m$;

② There is exactly one line through point $P$ that is perpendicular to both $l$ and $m$;

③ There is exactly one line through point $P$ that intersects both $l$ and $m$;

④ There is exactly one line through point $P$ that is skew to both $l$ and $m$.

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