
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
The point  $M$  varies on the segment  $AB$  that measures  $2$  m.
a) Find the equation and the graphical representation of the locus of the points of the plane whose coordinates,  $x$ , and  $y$ , are, respectively, the areas of the squares of sides  $AM$  and  $MB$  .
b) Find out what kind of curve it is. (Suggestion: make a  $45^o$  axis rotation).
c) Find the area of the enclosure between the curve obtained and the coordinate axes.

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