
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
$ABCD$ is a rectangular sheet of paper that has been folded so that corner $A$ is matched with point $A'$ on edge $CD$. The crease is $EF$, where $E$ is on $AB$ and $F$ is on $CD$. Given $AF = 10$, $AE = 7$, and $DF = 2$, determine the perimeter of rectangle $ABCD$. The perimeter is expressed as $m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

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