
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 a cube where three of the edges are $\overline{AB}, \overline{BC},$ and $\overline{CD}$, with $\overline{AD}$ as an interior diagonal. Points $P, Q,$ and $R$ are on $\overline{AB}, \overline{BC},$ and $\overline{CD}$ respectively, such that $AP = 3, PB = 17, BQ = 10,$ and $CR = 5.$ What is the area of the polygon formed by the intersection of plane $PQR$ and the cube?

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