
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
There are 200 computers in a computer center, with some of them connected by a total of 345 cables. A "cluster" is defined as a set of computers such that a signal can travel from any computer in the set to any other computer in the set, possibly through intermediate computers. Originally, all the computers formed one cluster. However, one night an evil hacker cut several cables, resulting in 8 clusters. Find the maximum possible number of cables that were cut.

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