
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
Consider a set of points arranged in a grid with each point spaced one unit apart, both horizontally and vertically. Determine the number of square units enclosed by the polygon formed by connecting the following sequence of points:
[asy]
size(1inch, 1inch);
pair a=(0,0), b=(10,0), c=(20,0), d=(30,10);
pair e=(0,20), f=(10,20), g=(20,30), h=(10,30);
pair i=(0,30), j=(20,10), k=(30,20), l=(10,10);
dot(a);
dot(b);
dot(c);
dot(d);
dot(e);
dot(f);
dot(g);
dot(h);
dot(i);
dot(j);
dot(k);
dot(l);
draw(a--b--c--d--g--f--h--i--e--a);
[/asy]

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