
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
A sequence of vertices  $v_1,v_2,\ldots,v_k$  in a graph, where  $v_i=v_j$  only if  $i=j$  and  $k$  can be any positive integer, is called a  $\textit{cycle}$  if  $v_1$  is attached by an edge to  $v_2$ ,  $v_2$  to  $v_3$ , and so on to  $v_k$  connected to  $v_1$ .  Rotations and reflections are distinct:  $A,B,C$  is distinct from  $A,C,B$  and  $B,C,A$ .  Supposed a simple graph  $G$  has  $2013$  vertices and  $3013$  edges.  What is the minimal number of cycles possible in  $G$ ?

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