
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
A triangular board with a base of 8 inches and a height of 10 inches is nailed together with a rectangular board that is 5 inches wide. They cross each other forming an X with an angle of 45 degrees at their point of intersection. After painting, if the boards are separated, what is the area of the unpainted region on the triangular board? Assume the vertex of the triangle opposite the base aligns with the rectangle's width and the nails' impact is negligible.

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