
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 "Selling Oil," it is written that the old man placed a gourd on the ground with its mouth down and slowly poured oil through a spoon into a hole without wetting the coin. This demonstrates the old man's skillful technique, which is admirable. If the coin is a circle with a diameter of $c$ and has a square hole in the middle with a side length of $0.5c$, what is the probability that a drop of oil (assuming the drop is negligibly small) falls exactly into the hole?

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