
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, with no three collinear, define a unique conic section. For the five points \[(0,0), \; (0,4), \; (2,0), \; (2,4), \; (-1,2)\] determine the type of conic section and find the length of its minor axis if the conic section is an ellipse with axes parallel to the coordinate axes.

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