
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
Let \( x \) be a natural number. If a sequence of natural numbers \( x_{0}=1, x_{1}, x_{2}, \cdots, x_{l}=x \) satisfies \( x_{i-1}<x_{i} \) and \( x_{i-1} \mid x_{i} \) for \( i=1,2,\cdots,l \), then \(\{x_{0}, x_{1}, x_{2}, \cdots, x_{l}\}\) is called a divisor chain of \( x \), and \( l \) is the length of this divisor chain. \( L(x) \) and \( R(x) \) represent the length of the longest divisor chain of \( x \) and the number of such longest chains, respectively. 

For \( x = 5^{k} \cdot 31^{m} \cdot 1990^{n} \) (where \( k, m, n \) are natural numbers), find \( L(x) \) and \( R(x) \).

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