
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
Find the smallest natural number \( l \) such that in a graph with \( n \) vertices (\( n \geq 3 \)), if the number of edges is more than \( \frac{1}{2} n \sqrt{n-1} \), there is a cycle of length less than \( l \).

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