
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
Given a 101-vertex simple connected graph $G(V, E)$, where every edge is contained in a cycle of length not exceeding $c(G)$, find the minimum possible value of $c(G) + |E(G)|$.

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