
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
Calculate the area of the shaded region in the following scenario:[asy]
size(200);
draw((0,0)--(50,0)--(50,50)--(0, 50)--cycle);
dot((50,0));dot((0,0));dot((15,0));dot((50,30));dot((50,50)); dot((35,50));dot((0,50));dot((0,15));
filldraw((0,0)--(15,0)--(50,30)--(50,50)--(35,50)--(0,15)--(0,0)--cycle, lightgray);
draw((0,0) -- (50,0), EndArrow);
draw((0,0) -- (-40,0), EndArrow);
draw((0,0) -- (0,60), EndArrow);
draw((0,0) -- (0,-40), EndArrow);
label("(0,0)",(0,0), SW, fontsize(8));
label("(15,0)",(15,0), S, fontsize(8));
label("(50,0)",(50,0), S, fontsize(8));
label("(50,30)",(50,30), E, fontsize(8));
label("(35,50)",(35,50), N, fontsize(8));
label("(0,50)",(0,50), W, fontsize(8));
label("(50,50)",(50,50), NE, fontsize(8));
label("(0,15)",(0,15), W, fontsize(8));
[/asy]

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