
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 solid right prism $ABCDEF$ has a height of $20,$ as shown. Its bases are equilateral triangles with side length $10.$ Points $X,$ $Y,$ and $Z$ are the midpoints of edges $AC,$ $BC,$ and $DC,$ respectively. A part of the prism is sliced off with a straight cut through points $X,$ $Y,$ and $Z.$ Determine the surface area of solid $CXYZ,$ the part that was sliced off.

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