
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. We call  $\{x_0,x_1,\dots ,x_l\}$  a *factor link*of  $x$  if the sequence  $\{x_0,x_1,\dots ,x_l\}$  satisfies the following conditions:
(1)  $x_0=1, x_l=x$ ;
(2)  $x_{i-1}<x_i, x_{i-1}|x_i, i=1,2,\dots,l$  .
Meanwhile, we define  $l$  as the length of the *factor link*  $\{x_0,x_1,\dots ,x_l\}$ . Denote by  $L(x)$  and  $R(x)$  the length and the number of the longest *factor link* of  $x$  respectively. For  $x=5^k\times 31^m\times 1990^n$ , where  $k,m,n$  are natural numbers, find the value of  $L(x)$  and  $R(x)$ .

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