
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 square in an array of unit squares, part of which is shown. The first ring of squares around this center square, which is at a distance of 1 unit from the center, contains 8 unit squares. The second ring, at a distance of 2 units from the center, contains 16 unit squares. If the pattern of increasing distance continues, what is the number of unit squares in the $50^{th}$ ring, if each ring’s distance from the center increases linearly (i.e., $n^{th}$ ring is at $n$ units from the center), and every second ring starting from the first is colored red?

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