
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
The cube $ABCDEFGH$ has edge length 1. The midpoint of edge $AE$ is $P$, and the center of face $BCGF$ is $R$.

a) What is the area of the planar section that intersects the cube through points $P$, $B$, and $R$?

b) The aforementioned plane cuts the cube into two solids. What is the ratio of their volumes?

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