
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 curvature of a polyhedron is $2 \pi$ minus the sum of the face angles (the internal angles of the faces of the polyhedron). For example, a cube's face angle is $2 \pi - 3 \times \frac{\pi}{2} = \frac{\pi}{2}$, and its total curvature is $\frac{\pi}{2} \times 8 = 4 \pi$. What is the total curvature of a polyhedron with four triangular faces and one square face?

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