
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 theorem states that given any five points in the plane, with no three on the same line, there is a unique conic section (ellipse, hyperbola, or parabola) which passes through all five points. Consider the five points \[ (1, 0), \; (1, 3), \; (4, 0), \; (4, 3), \; (6, \tfrac32) \]. There is an ellipse whose axes are parallel to the coordinate axes that passes through these points. Determine the length of its minor axis.

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