
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
A positive integer n is called *primary divisor* if for every positive divisor  $d$  of  $n$  at least one of the numbers  $d - 1$  and  $d + 1$  is prime. For example,  $8$  is divisor primary, because its positive divisors  $1$ ,  $2$ ,  $4$ , and  $8$  each differ by  $1$  from a prime number ( $2$ ,  $3$ ,  $5$ , and  $7$ , respectively), while  $9$  is not divisor primary, because the divisor  $9$  does not differ by  $1$  from a prime number (both  $8$  and  $10$  are composite). Determine the largest primary divisor number.

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