
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

During a ritual dance, a shaman from an island tribe throws three thin straight sticks of equal length, connected to form a shape resembling the letter "Π", into the air. The neighboring sticks are connected by a short string and can freely rotate relative to each other. The sticks fall onto the sand, forming a random shape. If a self-intersection occurs (the first and third sticks intersect), the tribe predicts poor harvests and various misfortunes for the coming year. If there is no self-intersection, the year is expected to be prosperous, plentiful, and happy. Find the probability that the sticks will predict good fortune for the year 2017.

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