
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 \( X \) be the collection of all functions \( f:\{0,1, \ldots, 2016\} \rightarrow \{0,1, \ldots, 2016\} \). Compute the number of functions \( f \in X \) such that
\[ 
\max _{g \in X}\left(\min _{0 \leq i \leq 2016}(\max (f(i), g(i)))-\max _{0 \leq i \leq 2016}(\min (f(i), g(i)))\right) = 2015.
\]

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