
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 a finite graph  $G$ , let  $f(G)$  be the number of triangles and  $g(G)$  the number of tetrahedra formed by edges of  $G$ . Find the least constant  $c$  such that \[g(G)^3\le c\cdot f(G)^4\] for every graph  $G$ .

*Proposed by Marcin Kuczma, Poland*

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