
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 edge length $3$ inches is iced on all faces. The cake is cut from a corner point directly to the midpoint of the opposite face's edge and similarly from the same corner point to the midpoint of another adjacent face's edge, forming a triangular top view. Let $c$ be the volume in cubic inches of the triangular cake piece and $s$ the total area in square inches of icing on this piece. Calculate $c+s$.
A) $21$
B) $22.5$
C) $23.5$
D) $24$
E) $26$

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