
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 each side of length $s$. Inside the hexagon, there is a smaller equilateral triangle whose vertices are the midpoints of three non-consecutive sides of the hexagon. If a dart is thrown at the board and lands randomly, calculate the probability that it falls within the smaller equilateral triangle.

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