
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 with segment $AC$ serving as a diameter of the circle. If $m\angle DAC = 15^\circ$ and $m\angle BAC = 60^\circ$, determine the ratio of the area of $ABCD$ to the area of the circle. The ratio can also be expressed in the form $\frac{a + \sqrt{b}}{c\pi}$, where $a$, $b$, and $c$ are positive integers. What is the value of $a+b+c$?

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