
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
On a standard coordinate plane, a square is positioned such that its vertices might not necessarily align with axis lines, and its sides are not parallel to the axes. Given that we are interested in finding the approximate area of the largest square containing exactly five lattice points within its interior, calculate this area.
A) 10.0
B) 10.23
C) 10.47
D) 10.5

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