
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
From a right prism with a square base with side length \( L_{1} \) and height \( H \), we extract a frustum of a pyramid, not necessarily right, with square bases, side lengths \( L_{1} \) (for the lower base) and \( L_{2} \) (for the upper base), and height \( H \). The two pieces obtained are shown in the following image.

If the volume of the frustum of the 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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