
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
In plane geometry, we have the theorem that "two lines perpendicular to the same line are parallel". Try to replace the lines (partially or entirely) with planes in this theorem, and write out a proposition that holds in space.

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