
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 edge length 30 units. Points $P, Q,$ and $R$ are on $\overline{AB}, \overline{BC},$ and $\overline{CD},$ respectively, forming the edges of the cube. It is given that $AP = 10, PB = 20, BQ = 20,$ and $CR = 15.$ What is the area of the polygon that is the intersection of the plane $PQR$ and the cube?

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