
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
Given a square in the coordinate plane with vertices at \((0, 0)\), \((3030, 0)\), \((3030, 3030)\), and \((0, 3030)\), find the value of \(d\) to the nearest tenth, where the probability that a randomly chosen point within the square is within \(d\) units of a lattice point is \(\frac{3}{4}\).

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