
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 $3,~ 6$, and $18$, respectively. 
If vertex angles $B$ and $C$ are obtuse and $\cos C = - \sin B =\frac{4}{5}$, then compute the length of side $AD$.
A) 16.8
B) 17.9
C) 18.2
D) 18.5
E) 19.0

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