
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 dart board, the outer circle has a radius of $10$ units, and the inner circle has a radius of $5$ units. Three radii divide each circle into three congruent regions. Region values for scoring are as follows:
- Inner regions: 0, 3, 5 (where one sector is designated as a non-scoring "0" point sector)
- Outer regions: 4, 6, 3

A dart's landing region depends proportionally on the area it covers. If two darts land on this dartboard, what’s the probability that the sum of the scores from the darts is odd?
A) $\frac{2}{9}$
B) $\frac{1}{3}$
C) $\frac{4}{9}$
D) $\frac{1}{2}$
E) $\frac{2}{3}$

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