
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 quadrilaterals there exists a point within the quadrilateral that is equidistant from all four vertices:

a) A rectangle
b) A regular pentagon 
c) A rhombus that is not a square
d) An equilateral triangle
e) A general trapezoid that has congruent base angles
a) 0
b) 1
c) 2
d) 3
e) 4

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