
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
In Ouyang Xiu's "The Oil Peddler," it is written: "(The peddler) took a gourd and placed it on the ground, covered its mouth with money, then slowly poured oil with a ladle, the oil dripped into the hole where the money went in, yet the money remained dry." The skill of the oil peddler was truly amazing. If the copper coin is a circular surface with a diameter of $3cm$, and in the middle, there is a square hole with a side length of $1cm$. If a drop of oil (negligible in size) is randomly dripped onto the copper coin, then the probability that the oil drop falls into the hole is ____.

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