
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
In the 18th century, Euler discovered through research that for convex polyhedra, the number of faces $F$, the number of vertices $V$, and the number of edges $E$ satisfy an equation. Please study some of the geometric bodies you are familiar with (such as triangular pyramids, triangular prisms, cubes, etc.), and deduce the relationship equation between $F$, $V$, and $E$.

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