
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
Amy decided to further decorate a square clock face by painting a circular dartboard such that the circle is centered at the center of the square, and touches the midpoints of the square's sides. If $t'$ is the area of a triangular region formed by the lines from the circle's center to the angles at 12 o'clock and 1 o'clock, and $q'$ is the area of a semi-circular region between 1 o'clock and 2 o'clock, calculate the ratio $\frac{q'}{t'}$. Assume the side length of the square is 4 units.
A) $\frac{\pi}{2}$  
B) $\frac{\pi}{4}$  
C) $\frac{\pi}{3}$  
D) $2\pi$

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