
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 $W_1,W_2,\ldots,W_m$, and $150$ edges. Each vertex $W_j$ is intersected by a plane $Q_j$ that cuts all edges connected to $W_j$. These cuts produce $m$ pyramids and a new polyhedron $T$. Assuming no two planes intersect inside or on $S$, determine the number of edges on polyhedron $T$.

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