
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
A point is chosen at random within a rectangle in the coordinate plane whose vertices are $(0, 0), (1500, 0), (1500, 2500),$ and $(0, 2500)$. The rectangle covers an area of $3,750,000$ square units. Calculate the radius $d$ such that the probability that the point is within $d$ units of any lattice point is $\tfrac{1}{6}$.
**A)** 0.1
**B)** 0.2
**C)** 0.3
**D)** 0.4

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