
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?

[asy]
draw((0,0)--(9,16)--(33,16)--(9,0)--cycle,black+linewidth(1));
draw((9,16)--(9,0),black+linewidth(1));
draw((0,0)--(33,16),black+linewidth(1));
draw((9,0)--(9,0.5)--(8.5,0.5)--(8.5,0)--cycle,black+linewidth(1));
draw((9,16)--(9.5,16)--(9.5,15.5)--(9,15.5)--cycle,black+linewidth(1));
label("$A$",(0,0),NW);
label("$B$",(9,16),NW);
label("$C$",(33,16),E);
label("$D$",(9,0),SE);
label("15 cm",(0,0)--(9,16),NW);
label("9 cm",(0,0)--(9,0),S);
label("24 cm",(9,0)--(33,16),SE);
[/asy]

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