
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, some of which are connected by cables, with a total of 345 cables used. We define a "cluster" as a set of computers such that a signal can travel from any computer in the set to all other computers in the set, possibly through intermediate computers. Initially, all the computers formed a single cluster. One night, a malicious hacker cut several cables, resulting in the formation of 8 clusters. Find the maximum possible number of cables that were cut.

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