
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
A positive integer  $n$  is known as an *interesting* number if  $n$  satisfies
\[{\  \{\frac{n}{10^k}} \} > \frac{n}{10^{10}} \] 
for all  $k=1,2,\ldots 9$ .
Find the number of interesting numbers.

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