
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
Given a square with a side of 5 cm. The vertices of a second square are located on the four sides of the first square; the vertices of a third square are located on the four sides of the second square, and so on. For what minimum natural number \( n \) will the sum of the areas of the first \( n \) squares be guaranteed to be more than 49 cm\(^2\)?

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