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[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

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[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

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system
A bagel is a loop of \( 2a + 2b + 4 \) unit squares which can be obtained by cutting a concentric \( a \times b \) hole out of an \( (a+2) \times (b+2) \) rectangle, for some positive integers \( a \) and \( b \). (The side of length \( a \) of the hole is parallel to the side of length \( a+2 \) of the rectangle.)

Consider an infinite grid of unit square cells. For each even integer \( n \geq 8 \), a bakery of order \( n \) is a finite set of cells \( S \) such that, for every \( n \)-cell bagel \( B \) in the grid, there exists a congruent copy of \( B \) all of whose cells are in \( S \). (The copy can be translated and rotated.) We denote by \( f(n) \) the smallest possible number of cells in a bakery of order \( n \).

Find a real number \( \alpha \) such that, for all sufficiently large even integers \( n \geq 8 \), we have
$$
\frac{1}{100} < \frac{f(n)}{n^{\alpha}} < 100.
$$

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