
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 if the diagonal forms a right angle with one of the adjacent sides?

[asy]
draw((0,0)--(6,6)--(14,1)--(8,-7)--cycle,linewidth(0.7));
draw((0,0)--(14,1),dashed);
label("9",(3,3),NW);
label("11",(10,3.5),NE);
label("18",(11, -3),SE);
label("14",(4,-3),SW);
[/asy]

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