
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
On a $4 \times 4$ grid of squares, Bella the bunny begins in the central square (square (2,2) or (3,3)), hopping in one of four cardinal directions (up, down, left, right) upon each move. Like Frieda, Bella wraps around to the opposite edge when hopping off the grid. Bella makes at most five hops and stops if she lands on an edge square (any square not central or directly adjacent to a central square). What is the probability that Bella reaches an edge square in any of her five hops?
A) $\frac{1}{2}$
B) $\frac{3}{4}$
C) $\frac{7}{8}$
D) $\frac{15}{16}$
E) $\frac{31}{32}$

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