
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
Let \( k \) be a positive integer and \( f(k) \) a function such that if \(\frac{k-1}{k}=0.k_1 k_2 k_3 \ldots\), then \( f(k) = \overline{k_1 k_2 k_3} \). For example, \( f(3) = 666 \) because \(\frac{3-1}{3} = 0.666 \ldots \). Find the value of \( D = f(f(f(f(f(112))))) \).

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