
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 \( x_0 = 1, x_1, x_2, \cdots, x_{t-1}, x_t = x \) satisfies \( x_{i-1} \mid x_i \) and \( x_{t-1} < x_i \) for \( i = 1, 2, \cdots, t \), then \( \{x_0, x_1, \cdots, x_t\} \) is called a factor chain of \( x \) and \( t \) is the length of this factor chain. \( T(x) \) and \( R(x) \) represent the length of the longest factor chain of \( x \) and the number of such longest factor chains, respectively.

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

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