
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
There are two cylinders whose volume ratio is $5: 8$. Their lateral surfaces can be unfolded into identical rectangles. If the length and width of this rectangle are both increased by 6, its area increases by 114. What is the area of this rectangle?

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