
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
We call a real number  $x$  with  $0 < x < 1$  *interesting* if  $x$  is irrational and if in its decimal writing the first four decimals are equal. Determine the least positive integer  $n$  with the property that every real number  $t$  with  $0 < t < 1$  can be written as the sum of  $n$  pairwise distinct interesting numbers.

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