
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, \( AB = 14\text{ cm}, \) \( DC = 21\text{ cm}, \) and \( AD = 6\text{ cm}. \) What is the length of \( AC, \) to the nearest tenth of a centimeter?

[asy]
draw((0,0)--(6,14)--(22,14)--(6,0)--cycle,black+linewidth(1));
draw((6,14)--(6,0),black+linewidth(1));
draw((0,0)--(22,14),black+linewidth(1));
draw((6,0)--(6,0.5)--(5.5,0.5)--(5.5,0)--cycle,black+linewidth(1));
draw((6,14)--(6.5,14)--(6.5,13.5)--(6,13.5)--cycle,black+linewidth(1));
label("$A$",(0,0),NW);
label("$B$",(6,14),NW);
label("$C$",(22,14),E);
label("$D$",(6,0),SE);
label("14 cm",(0,0)--(6,14),NW);
label("6 cm",(0,0)--(6,0),S);
label("21 cm",(6,0)--(22,14),SE);
[/asy]

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