
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 any five points in the plane, no three collinear, determine a unique conic section. For points \[(-\tfrac52, 1), \; (0,0), \;(0,3),\; (4,0),\; (4,3)\], find the conic section type and the length of its major axis, assuming it is an ellipse with axes parallel to the coordinate axes.

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