
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

Find the maximum volume (correct to three decimal places) of a regular quadrilateral frustum with the upper base length and the slant height both equal to 1.

Note: If the upper base area of the regular quadrilateral frustum is \(S_{1}\), the lower base area is \(S_{2}\), and the height is \(h\), then its volume is given by
$$
V=\frac{1}{3} h\left(S_{1}+S_{2}+\sqrt{S_{1} S_{2}}\right) .
$$

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