
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
We randomly throw a 10-filér coin onto a $40 \times 40$ cm chessboard. What is the probability that the coin:

a) will be entirely inside one square?

b) will partially cover one and only one square edge?

c) will partially cover two square edges but not a vertex?

d) will cover a vertex? (The diameter of the 10-filér coin is $19 \mathrm{~mm}$).

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