
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 in the diagram below:
```
[asy]
size(250);
draw((0,0)--(40,0)--(40,40)--(0, 40)--cycle);
dot((40,0));dot((0,0));dot((15,0));dot((40,25));dot((40,40)); dot((25,40));dot((0,40));dot((0,15));
filldraw((0,0)--(15,0)--(40,25)--(40,40)--(25,40)--(0,15)--(0,0)--cycle, lightgray);
draw((0,0)--(70,0),EndArrow);
draw((0,0)--(-40,0),EndArrow);
draw((0,0)--(0,70),EndArrow);
draw((0,0)--(0,-40),EndArrow);
label("(0,0)",(0,0), SW, fontsize(10));
label("(15,0)",(15,0), S, fontsize(10));
label("(40,0)",(40,0), S, fontsize(10));
label("(40,25)",(40,25), E, fontsize(10));
label("(25,40)",(25,40), N, fontsize(10));
label("(0,40)",(0,40), W, fontsize(10));
label("(40,40)",(40,40), NE, fontsize(10));
label("(0,15)",(0,15), W, fontsize(10));
[/asy]
```

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