
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 $24,$ as shown. Its bases are equilateral triangles with side length $18.$ Points $X,$ $Y,$ and $Z$ are located along the edges $AC,$ $BC,$ and $DC,$ respectively, each a third of the way from points $A,$ $B,$ and $D.$ A part of the prism above is sliced off with a straight cut through points $X,$ $Y,$ and $Z.$ Determine the surface area and the volume of solid $CXYZ,$ the part that was sliced off.
[asy]
pair A, B, C, D, E, F, X, Y, Z;
A=(0,0);
B=(18,0);
C=(9,-9*sqrt(3)/2);
D=(9,-36);
E=(0,-24);
F=(18,-24);
X=(2*A+C)/3;
Y=(2*B+C)/3;
Z=(2*D+C)/3;
draw(A--B--C--A--E--D--F--B--C--D);
draw(X--Y--Z--X, dashed);
label("$A$", A, NW);
label("$B$", B, NE);
label("$C$", C, N);
label("$D$", D, S);
label("$E$", E, SW);
label("$F$", F, SE);
label("$X$", X, SW);
label("$Y$", Y, SE);
label("$Z$", Z, SE);
label("18", (A+B)/2, dir(90));
label("24", (B+F)/2, dir(0));
[/asy]

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