
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]


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From a right prism with a square base of side length \(L_{1}\) and height \(H\), a truncated pyramid is extracted. The truncated pyramid, which is not necessarily right, has square bases with side lengths \(L_{1}\) (for the bottom base) and \(L_{2}\) (for the top base), and height \(H\). 

If the volume of the truncated pyramid is \(\frac{2}{3}\) of the total volume of the prism, what is the value of \( \frac{L_{1}}{L_{2}}\)?

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