
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
A cube has vertices at $(0,0,0),$ $(0,0,5),$ $(0,5,0),$ $(0,5,5),$ $(5,0,0),$ $(5,0,5),$ $(5,5,0),$ and $(5,5,5)$. A plane intersects the cube at points $P=(0,3,0),$ $Q=(2,0,0),$ $R=(2,5,5),$ and two other points. Determine the distance between these two additional points where the plane intersects the cube.

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