
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
If an $n$-vertex graph $G$ does not contain $K_{k}$, then the maximum number of edges in $G$ is:
$$
M(n, k)=\frac{k-2}{k-1} \cdot \frac{n^{2}-r^{2}}{2}+C_{r}^{2},
$$

where $r \equiv n \pmod{k-1}$, and $0 \leq r \leq k-2$.

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