
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
There is a magical grid paper of dimensions \(2000 \times 70\), initially all cells are grey. A painter starts at a certain cell and paints it red. Every second, the painter takes two steps: one cell to the left and one cell downwards, and paints the cell he lands on red. If the painter stands in the leftmost column and needs to step left, he teleports to the rightmost cell of the same row; if he stands in the bottom row and needs to step downwards, he teleports to the top cell of the same column. After several moves, the painter returns to the cell he started from. How many red cells are there on the grid at that moment?

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