
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  $ good$  if it can be uniquely written simultaneously as  $ a_1\plus{}a_2\plus{}...\plus{}a_k$  and as  $ a_1 a_2...a_k$ , where  $ a_i$  are positive integers and  $ k \ge 2$ . (For example,  $ 10$  is good because  $ 10\equal{}5\plus{}2\plus{}1\plus{}1\plus{}1\equal{}5 \cdot 2 \cdot 1 \cdot 1 \cdot 1$  is a unique expression of this form). Find, in terms of prime numbers, all good natural numbers.

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