
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
Given a square  $ABCD$  with two consecutive vertices, say  $A$  and  $B$  on the positive  $x$ -axis and positive  $y$ -axis respectively. Suppose the other vertice  $C$  lying in the first quadrant has coordinates  $(u , v)$ . Then find the area of the square  $ABCD$  in terms of  $u$  and  $v$ .

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