
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
Today is December 19. We place the numbers 1, 2, 1, 9, composed of small shaded squares with side length 1, within a larger $8 \times 5$ rectangle. If we rotate the large rectangle by $180^{\circ}$, it becomes “6121”. If we overlay these two $8 \times 5$ large rectangles, the total number of overlapping shaded squares is $\qquad$.

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