
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
Determine how many different whole numbers could be the length of the diagonal (dashed line) in the following quadrilateral:

[asy]
draw((0,0)--(6,6)--(15,2)--(8,-9)--cycle,linewidth(0.7));
draw((0,0)--(15,2),dashed);
label("10",(3,3),NW);
label("12",(10.5,4),NE);
label("18",(11.5,-3.5),SE);
label("15",(4,-3.5),SW);
[/asy]

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