
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
Consider the set  $E = \{5, 6, 7, 8, 9\}$ . For any partition  ${A, B}$  of  $E$ , with both  $A$  and  $B$  non-empty, consider the number obtained by adding the product of elements of  $A$  to the product of elements of  $B$ . Let  $N$  be the largest prime number amonh these numbers. Find the sum of the digits of  $N$ .

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