
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 the square on the coordinate plane whose vertices are $(0, 0), (1000, 0), (1000, 1000),$ and $(0, 1000)$. The probability that the point falls either within a circle or a square (both centered at a lattice point) with side-length = radius = $d$ is $\tfrac{3}{4}$. Find $d$ to the nearest tenth.
**A)** $0.3$
**B)** $0.4$
**C)** $0.5$
**D)** $0.6$
**E)** $0.7$

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