
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
Given \( x \in \mathbb{N} \). If a sequence of natural numbers \( 1 = x_{0}, x_{1}, \cdots, x_{l} = x \) satisfies
\[ x_{i-1} < x_{i}, \quad x_{i-1} \mid x_{i}, \quad \text{for } i = 1, 2, \cdots, l, \]
then \(\{ x_{0}, x_{1}, x_{2}, \cdots, x_{l} \} \) is called a factor chain of \( x \), and \( l \) is the length of this factor chain.

Let \( L(x) \) and \( R(x) \) respectively represent the length of the longest factor chain of \( x \) and the number of such longest factor chains.

For \( x = 5^{k} \times 31^{m} \times 1990^{n} \) where \( k, m, n \in \mathbb{N} \), find \( L(x) \) and \( R(x) \).

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