
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 six points in the plane \((-\frac{5}{2}, 2), (0,0), (0,3), (4,0), (4,3), (2,4)\), with no three points collinear, there is a unique conic section passing through all these points. Propose that this conic section is an ellipse centered at \((2, \frac{3}{2})\) with its axes parallel to the coordinate axes. Find the length of the minor axis of this ellipse.

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