
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
A convex polyhedron S has vertices U1, U2, …, Um, and 120 edges. This polyhedron is intersected by planes Q1, Q2, …, Qm, where each plane Qk intersects only those edges that are connected to vertex Uk. No two planes intersect within the volume or on the surface of S. As a result, m pyramids are formed along with a new polyhedron T. Determine the number of edges that polyhedron T now possesses.

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