
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 dark rectangle of dimensions 2x3 units at the center of an array of unit squares, part of which is shown. The first ring of squares around this center rectangle contains more unit squares compared to a center square. For subsequent rings, if this process is continued, what is the number of unit squares in the $100^{th}$ ring around this center rectangle?

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