
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 square garden and surrounding walkways arranged in rings. Each ring represents an additional layer of walkway around the garden. The area of the garden (first square) is 9 square meters. Each subsequent walkway ring increases uniformly in width. Suppose the first ring around the garden is 16 square meters in area. Calculate the area of the $50^{th}$ ring.

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