
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
Let  $ABC$  be a non-equilateral triangle with integer sides. Let  $D$  and  $E$  be respectively the mid-points of  $BC$  and  $CA$  ; let  $G$  be the centroid of  $\Delta{ABC}$ . Suppose,  $D$ ,  $C$ ,  $E$ ,  $G$  are concyclic. Find the least possible perimeter of  $\Delta{ABC}$ .

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