
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 conic section permeating through the five given points \[(0,0), \; (0,2), \; (3,0), \; (3,2), \; (\frac{3}{2}, 3)\] in the plane, none of which happen to be collinear, is noted to be an ellipse with its axes parallel to the coordinate axes. Determine the length of its minor axis.

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