
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
In the cells of a \(75 \times 75\) table, pairwise distinct natural numbers are placed. Each of them has no more than three different prime divisors. It is known that for any number \(a\) in the table, there exists a number \(b\) in the same row or column such that \(a\) and \(b\) are not coprime. What is the maximum number of prime numbers that can be in the table?

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