
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
Let us call a positive integer  $k{}$  interesting if the product of the first  $k{}$  primes is divisible by  $k{}$ . For example the product of the first two primes is  $2\cdot3 = 6$ , it is divisible by 2, hence 2 is an interesting integer. What is the maximal possible number of consecutive interesting integers?

*Boris Frenkin*

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