
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 are given a coin of diameter  $\frac{1}{2}$  and a checkerboard of  $1\times1$  squares of area  $2010\times2010$ . We toss the coin such that it lands completely on the checkerboard. If the probability that the coin doesn't touch any of the lattice lines is  $\frac{a^2}{b^2}$  where  $\frac{a}{b}$  is a reduced fraction, find  $a+b$ 

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