
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
Find the greatest natural number  $n$  such there exist natural numbers  $x_{1}, x_{2}, \ldots, x_{n}$  and natural  $a_{1}< a_{2}< \ldots < a_{n-1}$  satisfying the following equations for  $i =1,2,\ldots,n-1$ : \[x_{1}x_{2}\ldots x_{n}= 1980 \quad \text{and}\quad x_{i}+\frac{1980}{x_{i}}= a_{i}.\]

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