
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
Two points are chosen inside the square \(\{(x, y) \mid 0 \leq x, y \leq 1\}\) uniformly at random, and a unit square is drawn centered at each point with edges parallel to the coordinate axes. The expected area of the union of the two squares can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are relatively prime positive integers. Compute \(100a + b\).

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