
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
In some cells of a $1 \times 2100$ strip, a chip is placed in each cell. A number equal to the absolute difference between the number of chips to the left and to the right of this cell is written in each empty cell. It is known that all recorded numbers are different and non-zero. What is the smallest number of chips that can be placed in the cells?

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