
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
In quadrilateral ABCD, <span class="qseq"></span>AB = (6,1), BC = (x,y), CD = (-2,-3)<br /> (1) If <span class="qseq"></span>BC∥DA, find the relationship between x and y;<br /> (2) If BC∥DA and AC⊥BD, find the values of x and y, and the area of quadrilateral ABCD.

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