
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
Sides $AB,~ BC$, and $CD$ of quadrilateral $ABCD$ have lengths $6,~ 8$, and $15$, respectively. 
Vertex angles $B$ and $C$ are obtuse, and $\sin C = - \cos B = \frac{4}{5}$. Determine the length of side $AD$.
A) $25.5$
B) $26$
C) $30$
D) $31$
E) $35$

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