
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
Gabby the gecko begins her journey on a $4 \times 4$ grid of squares, with each hop moving her one square up, down, left, or right. She does not hop diagonally or consecutively in the same vertical or horizontal direction. The grid also has a "wrap around" feature, where moving off one edge brings her to the opposite side of the grid. Gabby starts from a center square, makes at most five hops at random under these rules, and stops hopping if she lands on an edge square. What is the probability that she reaches any edge square within the five hops?
$\textbf{A)} ~\frac{24}{64}\qquad\textbf{B)} ~\frac{27}{64}\qquad\textbf{C)} ~\frac{32}{64}\qquad\textbf{D)} ~\frac{35}{64}\qquad\textbf{E)} ~\frac{40}{64}$

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