
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 $Q$ has vertices $V_1,V_2,\ldots,V_n$, and $120$ edges. It is sliced by $n$ planes $P_1,P_2,\ldots,P_n$, such that each plane $P_k$ cuts all the edges emanating from vertex $V_k$ and each plane $P_k$ adds $2$ edges by forming new edges directly interconnecting any two newly created vertices from the cuts on any particular edge originating at $V_k$. No two planes intersect inside or on the surface of $Q$. After all slices, $n$ pyramids and a new polyhedron $R$ are formed. How many edges does $R$ have?
A) 720
B) 800
C) 840
D) 960
E) 1000

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