
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 $0 < v < u$. Define points as $A = (2u,v)$, and for transformations, let $B$ be the reflection of $A$ across the line $y = x$, $C$ be the reflection of $B$ across the y-axis, $D$ be the reflection of $C$ across the x-axis, and $E$ be the reflection of $D$ across the y-axis. The area of pentagon $ABCDE$ is $902$. Find $2u + v$.

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