
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 octagon with each side length equal to $2$ units. It is entirely covered with equilateral triangles, each side having length $1$ unit. Find the probability that a dart lands within one of these triangles sharing a side with the octagonal boundary.

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