
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 $a$ and $b$ be integers satisfying $0 < b < a$. Let $P = (a,b)$. Create points $Q$, $R$, $S$, and $T$ such that $Q$ is the reflection of $P$ across the line $y=x$, $R$ is the reflection of $Q$ across the y-axis, $S$ is the reflection of $R$ across the x-axis, and $T$ is the reflection of $S$ across the y-axis. If the area of pentagon $PQRST$ is $792$, find $a + b$.

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