
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 an oblique parallelepiped, the projection of a lateral edge onto the base plane is 5, and the height is 12. A cross-section perpendicular to the lateral edge is a rhombus with an area of 24 and a diagonal of 8. Find the lateral surface area and the volume of the parallelepiped.

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