
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 $5 \times 7$ grid where the area of each small square is 1, and there is 1 gray square. By appropriately selecting 4 grid points at the intersections of the horizontal and vertical lines, one can draw a rectangle with these 4 points as vertices that does not contain the gray square, does not intersect with the gray square, and has an area of 15. Find the number of such rectangles that can be drawn.

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