
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. [asy]
size(200);
draw((0,0)--(40,0)--(40,40)--(0, 40)--cycle);
dot((40,0));dot((0,0));dot((10,0));dot((40,30));dot((40,40)); dot((30,40));dot((0,40));dot((0,10));
filldraw((0,0)--(10,0)--(40,30)--(40,40)--(30,40)--(0,10)--(0,0)--cycle, lightgray);
draw((0,0)--(60,0),EndArrow);
draw((0,0)--(-30,0),EndArrow);
draw((0,0)--(0,50),EndArrow);
draw((0,0)--(0,-30),EndArrow);
label("(0,0)",(0,0), SW, fontsize(8));
label("(10,0)",(10,0), S, fontsize(8));
label("(40,0)",(40,0), S, fontsize(8));
label("(40,30)",(40,30), E, fontsize(8));
label("(30,40)",(30,40), N, fontsize(8));
label("(0,40)",(0,40), W, fontsize(8));
label("(40,40)",(40,40), NE, fontsize(8));
label("(0,10)",(0,10), W, fontsize(8));
[/asy]

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