
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
Shaq sees the numbers  $1$  through  $2017$  written on a chalkboard. He repeatedly chooses three numbers, erases them, and writes one plus their median. (For instance, if he erased  $-2, -1, 0$  he would replace them with  $0$ .) If  $M$  is the maximum possible final value remaining on the board, and if m is the minimum, compute  $M - m$ .

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