
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]


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In a tech company with $50$ employees, $35$ of whom use computers of brand X and the other $15$ use computers of brand Y, determine the maximum number of cables that can be installed between pairs of computers from different brands such that, by the end of the process, there exist at least $3$ completely interconnected subnetworks among the computers.

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