
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 a tent has a square shape with side length $a = 15 \mathrm{~m}$. The boundary of the base consists of 4 arcs and 4 straight segments. The centers of the arcs are at the vertices of the square, with radii $a, a, a/2, a/2$. The straight segments are the external common tangents of the neighboring arcs. There are columns at the vertices of the square, each with a height equal to the radius of the arc centered at its base. The tent fabric consists of 4 conical surfaces, each based on one of the arcs and apex at the top of the column above the arc’s center, as well as 5 planar quadrangles, with vertices at the tops of the columns and the endpoints of the tangent segments. Calculate the area of the tent fabric, the volume of the tent, and its average height (the ratio of its volume to its base area). Draw a possible unfolded view of the tent fabric in one piece.

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