
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 diamond-shaped center in an array of unit squares, part of which is shown. The first ring of squares around this diamond-shaped center contains 4 unit squares. The second ring contains 12 unit squares. If we continue this process, what is the number of unit squares in the $100^{th}$ ring, given that each subsequent ring grows in a pattern of adding 8 more squares than the previous ring?

[asy]
fill((-1,0)--(0,1)--(1,0)--(0,-1)--cycle,gray(0.8));
fill((-2,1)--(1,2)--(2,-1)--(-1,-2)--cycle,gray(0.6));
fill((0,0)--(0,0)--(0,0)--(0,0)--cycle,black);
for (int i=-3; i<4; ++i) {
draw((-3,i)--(3,i));
draw((i,-3)--(i,3));
}
[/asy]

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