
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
In the triangle depicted below, for $\angle A$ to be the largest angle of the triangle, it must be that $p<q<r$. What is the least possible value of $r-p$, expressed as a common fraction? 
\[
\text{Triangle configuration:}
\begin{array}{ccc}
& A & \\
& \hspace{1mm} & \\
B & ----- & C \\
\end{array}
\]
The side lengths are given as: $AB = x+6$, $AC = 2x$, and $BC = x+5$. Determine the least possible value of $r-p$.

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