
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 with an edge length of $3$ inches is iced on all faces. It is cut into four vertical pieces as shown in a top view, where $N$ is a point one-third of the way along a top edge from a corner. The piece whose top is a trapezoid $C$ contains $c$ cubic inches of cake and $s$ square inches of icing. Calculate $c+s$.
A) $30$
B) $33$
C) $36$
D) $39$

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