
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
For all integers \( r \) and \( n \) with \( r > 1 \), every graph \( G \) with \( n \) vertices and \(\operatorname{ex}(n, K^{r})\) edges, where \( G \) does not contain \( K^{r} \), is \( T^{r-1}(n) \).

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