
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
A rectangle has length $L$ and width $W$, and its area $A$ is given by $A = L \cdot W$. This rectangle is transformed into an equilateral triangle by cutting and rearranging its area with minimal waste, and the resulting triangle has the same area $A$. If the side of the equilateral triangle formed is $s$, determine the relation between $L, W,$ and $s$.

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