
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
Ouyang Xiu wrote in "The Oil Seller": The old man then placed a gourd on the ground, covered its mouth with a coin, and slowly ladled oil to drip through the coin into the gourd, with the oil entering the hole without wetting the coin. This demonstrates the saying "Excellence can be found in any profession," and the oil seller's skill is indeed astonishing. If the coin is a circle with a diameter of $2cm$ and has a square hole in the middle with a side length of $0.5cm$, if you randomly drop a drop of oil (ignoring the size of the oil drop) onto the coin, the probability that the oil exactly falls into the hole is ______.

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