
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 the diagonal represented by the dashed line?

[asy]
draw((0,0)--(6,6)--(15,2)--(9,-6)--cycle,linewidth(0.7));
draw((0,0)--(15,2),dashed);
label("9",(3,3),NW);
label("13",(10.5,4),NE);
label("18",(12, -2),SE);
label("15",(4.5,-3),SW);
[/asy]

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