
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 cubical cake with an edge length of $3$ inches is iced on all sides and top. The cake is cut vertically into three pieces from a point $M$, located one-third of the length from the corner $P$ along edge $PS$. Consider the triangle formed as the top view of one piece. If $M$ is derived from $P$ moving towards $S$ on the cube’s top face and the cutting lines are from $M$ to $Q$ and $M$ to $R$, what is the sum of the volume $c$ in cubic inches and the area $s$ in square inches of icing of this piece?
A) 17.7
B) 18.8
C) 19.8
D) 20.9
E) 21.5

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