
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 \( N \) be a natural number whose base-2016 representation is \( ABC \). Working now in base-10, what is the remainder when \( N - (A + B + C + k) \) is divided by 2015, if \( k \in \{ 1, 2, \ldots, 2015 \} \)?

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