
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
Given five points in the plane, no three of which lie on the same straight line, determine the type of conic section passing through the five points: \[ (-2, 1), \; (0,0), \; (0,3), \; (4,0), \; (4,3) \]. Assume the conic section's axes are parallel to the coordinate axes and find the length of its minor axis.

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