
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
In the base of the pyramid \(SABC D\) lies a quadrilateral \(ABCD\), where sides \(AD\) and \(BC\) are parallel. The side \(AB\) is equal to 4, the side \(BC\) is equal to 8, and the angle \(\angle ABC\) is \(60^\circ\). The edge \(SB\) is equal to \(8\sqrt{2}\). Find the volume of the pyramid, given that it is possible to draw two planes through the lines \(AD\) and \(BC\) that do not coincide with the base of the pyramid and intersect the pyramid along equal quadrilaterals.

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