
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
 $5.$ Let x be a real number with  $0<x<1$  and let  $0.c_1c_2c_3...$  be the decimal expansion of x.Denote by  $B(x)$  the set of all subsequences of  $c_1c_2c_3$  that consist of 6 consecutive digits.
For instance ,  $B(\frac{1}{22})={045454,454545,545454}$ Find the minimum number of elements of  $B(x)$  as  $x$  varies among all irrational numbers with  $0<x<1$ 

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