
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
Call a rational number *short* if it has finitely many digits in its decimal expansion. For a positive integer  $m$ , we say that a positive integer  $t$  is  $m-$ *tastic* if there exists a number  $c\in \{1,2,3,\ldots ,2017\}$  such that  $\dfrac{10^t-1}{c\cdot m}$  is short, and such that  $\dfrac{10^k-1}{c\cdot m}$  is not short for any  $1\le k<t$ . Let  $S(m)$  be the set of  $m-$ tastic numbers. Consider  $S(m)$  for  $m=1,2,\ldots{}.$  What is the maximum number of elements in  $S(m)$ ?

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