
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
In a rectangular prism, determine the number of propositions among 
Proposition 1: In a rectangular prism, there must exist a point equidistant from all vertices.
Proposition 2: In a rectangular prism, there must exist a point equidistant from all edges.
Proposition 3: In a rectangular prism, there must exist a point equidistant from all faces
that are necessarily true.

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