
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 \(\frac{10^t - 1}{c \cdot m}\) is short, and such that \(\frac{10^k - 1}{c \cdot m}\) is not short for any \( 1 \leq k < t \). 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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