
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 the center square in an array of unit squares. Around this square, suppose each ring starts with a base of four rectangles each increasing in size nonlinearly. Specifically, the first ring of squares around the center square has 12 unit squares (calculated as three unit squares added per side from previous layer). If we keep this pattern of increasing each side of the rectangle by three additional squares instead of one, what is the number of unit squares in the $50^{th}$ ring?

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