
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
The equation

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

is written on the board. We want to erase certain linear factors so that the remaining equation has no real solutions. Determine the smallest number of linear factors that need to be erased to achieve this objective.

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