
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
What is the number of square units in the area of the octagon below?

[asy]
unitsize(0.5cm);
defaultpen(linewidth(0.7)+fontsize(10));
dotfactor = 4;
int i,j;
for(i=0;i<=5;++i)

{

for(j=-4;j<=4;++j)

{

dot((i,j));

}

}

for(i=1;i<=5;++i)

{

draw((i,-1/3)--(i,1/3));

}
for(j=1;j<=4;++j)

{

draw((-1/3,j)--(1/3,j));

draw((-1/3,-j)--(1/3,-j));

}

real eps = 0.2;

draw((4,4.5+eps)--(4,4.5-eps));
draw((5,4.5+eps)--(5,4.5-eps));
draw((4,4.5)--(5,4.5));

label("1 unit",(4.5,5));

draw((5.5-eps,3)--(5.5+eps,3));
draw((5.5-eps,4)--(5.5+eps,4));
draw((5.5,3)--(5.5,4));

label("1 unit",(6.2,3.5));

draw((-1,0)--(6,0));
draw((0,-5)--(0,5));
draw((0,0)--(1,4)--(4,4)--(5,0)--(4,-4)--(1,-4)--cycle,linewidth(2));
[/asy]

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