
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
The base of an inclined parallelepiped is a rhombus with a side length of 60. A diagonal section plane passing through the longer diagonal of the base is perpendicular to the base's plane. The area of this section is 7200. Find the shorter diagonal of the base if the lateral edge is 80 and forms an angle of $60^\circ$ with the base plane.

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