
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 a graph \( G \) with \( n \) vertices, if it does not contain a complete graph \( K_{p} \) of order \( p \), then the number of edges in graph \( G \) satisfies
$$
|E| \leqslant\left(1-\frac{1}{p-1}\right) \frac{n^{2}}{2},
$$

where a complete graph \( K_{p} \) of order \( p \) is a graph with \( p \) vertices such that every pair of these \( p \) vertices is connected by an edge.

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