
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
Find the number of square units in the area of the shaded region given the following vertices: The square has vertices at (0,0), (40,0), (40,40), and (0, 40). Within this square, there are two unshaded triangles: one with vertices at (0,0), (15,0), and (40,25), and another with vertices at (25,40), (40,40), and (40,25). Additionally, there is a shaded triangle with vertices at (0,0), (0,15), and (15,0).

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