
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
We draw the diagonals from one vertex of a regular pentagon and then construct equilateral triangles outward over the sides between their endpoints. Folding the triangles upward along the diagonals and the mentioned side such that their free vertices meet, we obtain a three-sided pyramid. What is the volume of the pyramid?

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