
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 rectangular checkerboard contains half-inch per side squares. A square card, $2$ inches on all sides, is placed so that it covers portions of multiple small squares. Determine the maximum number of these half-inch squares the card can overlap.
A) 16 or 17
B) 18 or 19 
C) 20 or 21
D) 22 or 23
E) 24 or 25

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