
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
Point $M$ describes the arc of an ellipse between its two vertices. The length of the semi-major axis is $a$ and the length of the semi-minor axis is $b$.

Examine the variations of the quantities $x y$ and $x+y$, where $x$ and $y$ represent the distances of point $M$ from the minor and major axes, respectively.

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