
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
If we pick uniformly a random square of area 1 with sides parallel to the $x$ and $y$ axes that lies entirely within the 5-by-5 square bounded by the lines $x=0$, $x=5$, $y=0$, and $y=5$ (the corners of the square need not have integer coordinates), what is the probability that the point $(x, y)=(4.5, 0.5)$ lies within the square of area 1?

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