
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 $BC$. The crease is $EF$, where $E$ is on $AB$ and $F$ is on $CD$. The dimensions $AE=6, BE=15,$ and $CF=5$ are given. The perimeter of rectangle $ABCD$ is $m/n$, 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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