
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 shaped as a regular hexagon with a side length $s$. At the center of the board, there is an equilateral triangle whose vertices touch the midpoints of three non-adjacent sides of the hexagon. If a dart thrown at the board lands randomly anywhere on it, find the probability that it lands within the central equilateral triangle.

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