
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
For the quadrilateral shown, how many different whole numbers could be the length of diagonal $AC$?

[asy]
draw((0,0)--(4,6)--(11,2)--(6,-9)--cycle,linewidth(0.7));
draw((0,0)--(11,2),dashed);
label("7",(2,3),NW);
label("13",(7.5,4),NE);
label("15",(8.5, -3.5),SE);
label("10",(3,-3.5),SW);
[/asy]

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