
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. The region is within a square with vertices at (0,0), (40,0), (40,40), and (0,40). Within this square, there are three unshaded right triangles, one with vertices at (0,0), (10,0), and (0,10), another with vertices at (40,0), (40,30), and (25,0), and the third at (40,40), (20,40), and (40,20). Fill the remaining region and calculate its area.

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