
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
The integer  $n$  has exactly six positive divisors, and they are:  $1<a<b<c<d<n$ . Let  $k=a-1$ . If the  $k$ -th divisor (according to above ordering) of  $n$  is equal to  $(1+a+b)b$ , find the highest possible value of  $n$ .

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