
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
The isosceles trapezoid shown has side lengths as labeled. How long is segment AC? 

[asy]
unitsize(1.5mm);
defaultpen(linewidth(.7pt)+fontsize(10pt));
dotfactor=3;
pair A=(0,0), B=(25,0), C=(17,8), D=(8,8);
pair[] dots={A,B,C,D};

draw(A--B--C--D--cycle);
dot(dots);
label("A",A,SW);
label("B",B,SE);
label("C",C,NE);
label("D",D,NW);
label("10",midpoint(C--D),N);
label("11",midpoint(D--A),NW);
label("25",midpoint(A--B),S);
label("11",midpoint(B--C),NE);
[/asy]

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