
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 point  $(x,y)$  in the first quadrant lies on a line with intercepts  $(a,0)$  and  $(0,b)$ , with  $a,b > 0$ . Rectangle  $M$  has vertices  $(0,0)$ ,  $(x,0)$ ,  $(x,y)$ , and  $(0,y)$ , while rectangle  $N$  has vertices  $(x,y)$ ,  $(x,b)$ ,  $(a,b)$ , and  $(a,y)$ . What is the ratio of the area of  $M$  to that of  $N$ ?

*Proposed by Eugene Chen*

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