
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
A dart board is a regular hexagon divided into regions as shown. The center of the board is a smaller regular hexagon, and each of the six surrounding regions is a trapezoid. The side length of the larger hexagon is twice that of the smaller hexagon. If a dart thrown at the board is equally likely to land anywhere on the board, determine the probability that the dart lands within the center hexagon.

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