
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
On a modified dart board, the outer circle has radius 8 and the inner circle has radius 4. Radii divide each circle into three equal sections, with point values assigned as follows: inner regions are labeled as 3, 4, 4 and outer regions as 4, 3, 3. The dart hitting probability is proportional to the area. Calculate the probability that a single dart throw scores 3.
A) \(\frac{1}{3}\)
B) \(\frac{1}{2}\)
C) \(\frac{7}{12}\)
D) \(\frac{2}{3}\)
E) \(\frac{3}{4}\)

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