
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
Consider a right pyramid with a regular hexagonal base where each side of the base measures 8 cm. The peak of this pyramid is 15 cm above the center of its base. On top of this pyramid, there is another smaller inverted right pyramid with a pentagonal base where each side measures 5 cm and its peak is 10 cm below the peak of the first pyramid. What is the sum of the lengths of all the edges of the compound structure?

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