
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
Quadrilateral $ABCD$ is inscribed in a circle such that segment $AC$ is a diameter. If $m\angle DAC = 45^\circ$ and $m\angle BAC = 60^\circ$, calculate the ratio of the area of $ABCD$ to the area of the circle, expressed as $\frac{a+ \sqrt{b}}{c \pi}$, where $a$, $b$, and $c$ are positive integers. Determine $a+b+c$.

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