
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
In the diagram, \(AB = 15\text{ cm}\), \(DC = 24\text{ cm}\), and \(AD = 9\text{ cm}\). What is the length of \(AC\), to the nearest tenth of a centimeter?

\[
\text{[asy]}
\draw((0,0)--(9,20)--(33,20)--(9,0)--cycle,black+linewidth(1));
\draw((9,20)--(9,0),black+linewidth(1));
\draw((0,0)--(33,20),black+linewidth(1));
\draw((9,0)--(9,0.5)--(8.5,0.5)--(8.5,0)--cycle,black+linewidth(1));
\draw((9,20)--(9.5,20)--(9.5,19.5)--(9,19.5)--cycle,black+linewidth(1));
label("$A$",(0,0),NW);
label("$B$",(9,20),NW);
label("$C$",(33,20),E);
label("$D$",(9,0),SE);
label("15 cm",(0,0)--(9,20),NW);
label("9 cm",(0,0)--(9,0),S);
label("24 cm",(9,0)--(33,20),SE);
\text{[/asy]}
\]

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