
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
An isosceles trapezoid has side lengths as labeled below. Determine the length of segment AC.

\[
\text{[asy]}
\text{unitsize(1.5mm);}
\text{defaultpen(linewidth(.7pt)+fontsize(10pt));}
\text{dotfactor=3;}

\text{pair A=(0,0), B=(26,0), C=(17,12), D=(9,12);}
\text{pair[] dots={A,B,C,D};}

\text{draw(A--B--C--D--cycle);}
\text{dot(dots);}
\text{label("A",A,SW);}
\text{label("B",B,SE);}
\text{label("C",C,NE);}
\text{label("D",D,NW);}
\text{label("12",midpoint(C--D),N);}
\text{label("13",midpoint(D--A),NW);}
\text{label("26",midpoint(A--B),S);}
\text{label("13",midpoint(B--C),NE);}
\text{[/asy]}
\]

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