
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 quadrilateral $ABCD$, sides $AB, BC$, and $CD$ have lengths $3, 4$, and $12$ respectively. Vertex angles $B$ is obtuse and $\sin B = \frac{4}{5}$, while angle $C$ is acute and $\cos C = \frac{4}{5}$. Determine the length of side $AD$.
A) 8.9
B) 9.0
C) 9.1
D) 9.2
E) 9.3

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