
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

Consider the equation

$$
(x-1)(x-2) \ldots(x-2016) = (x-1)(x-2) \ldots(x-2016)
$$

written on a board. What is the smallest integer $k$ such that we can erase $k$ factors among these 4032 factors so that there is at least one factor remaining on each side of the equation and the equation no longer has any real solutions?

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