
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
Let  $u$  and  $v$  be integers satisfying  $0<v<u.$  Let  $A=(u,v),$  let  $B$  be the reflection of  $A$  across the line  $y=x,$  let  $C$  be the reflection of  $B$  across the y-axis, let  $D$  be the reflection of  $C$  across the x-axis, and let  $E$  be the reflection of  $D$  across the y-axis. The area of pentagon  $ABCDE$  is 451. Find  $u+v.$ 

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