
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
A quadrilateral is labeled with vertices $P$, $Q$, $R$, and $S$. The lengths of sides $PQ$, $QR$, $RS$, and $SP$ are given as $9$, $11$, $15$, and $14$ respectively. Calculate how many different whole numbers could represent the length of the diagonal $PR$.

[asy]
draw((0,0)--(6,6)--(14,2)--(8,-7)--cycle,linewidth(0.7));
draw((0,0)--(14,2),dashed);
label("9",(3,3),NW);
label("11",(10,4),NE);
label("15",(11, -2.5),SE);
label("14",(4,-3.5),SW);
[/asy]

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