
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 hexagon depicted below? The hexagon is now surrounded by a different configuration of triangles along each side, resulting in a more segmented area calculation.

[asy]
unitsize(0.6cm);
defaultpen(linewidth(0.7)+fontsize(10));
dotfactor = 4;
fill((4,0)--(4,4)--(3,4)--cycle,lightgray);
fill((4,0)--(4,-4)--(3,-4)--cycle,lightgray);
fill((0,0)--(0,4)--(1,4)--cycle,lightgray);
fill((0,0)--(0,-4)--(1,-4)--cycle,lightgray);

int i,j;
for(i=0;i<=4;++i){
    for(j=-4;j<=4;++j){
        dot((i,j));
    }
}
draw((-1,0)--(5,0)); // X-axis
draw((0,-5)--(0,5)); // Y-axis
draw((0,0)--(1,4)--(3,4)--(4,0)--(3,-4)--(1,-4)--cycle,linewidth(1.5)); // Hexagon

label("1 unit",(3.5,4.5),N);
label("1 unit",(5,2.5),E);

[/asy]

Each outer segmented triangle has 1 base unit and 4 height units, versus 3 height units in the original.

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