
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 square in the plane has vertices at lattice points. What is the area of one such square that contains exactly four lattice points within its boundary (including the vertices)? Assume that one lattice point exactly falls on a vertex and two other unique points fall on different sides (not corners) of the square.
A) 0.5
B) 1
C) 2
D) 4

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