
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
When the natural number \( n \geq 2 \) is the smallest, find the integers \( a_1, a_2, \ldots, a_n \) that satisfy the following equations: 
\[ a_1 + a_2 + \cdots + a_n = a_1 \cdot a_2 \cdots a_n = 1990. \]

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