
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
Determine for how many of the following types of quadrilaterals there exists a point in the plane of the quadrilateral that is equidistant from all four vertices of the quadrilateral:

a. a square  
b. a rectangle that is not a square  
c. a rhombus that is not a square  
d. a parallelogram that is not a rectangle or a rhombus  
e. a kite with diagonals perpendicular to each other
A) 0  
B) 1  
C) 2  
D) 3  
E) 4

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