
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
Frieda the frog starts her journey on a \(4 \times 4\) grid from one of the central squares, being the second square of the second row. Each hop Frieda makes can either be up, down, left, or right, and if a hop would take her off the grid, she wraps around to the opposite side. If she lands on any boundary square, she will stop hopping. What is the probability that she will reach any boundary square within five hops?
A) \( \frac{1}{2} \)
B) \( \frac{105}{128} \)
C) \( \frac{121}{128} \)
D) \( \frac{125}{128} \)
E) \( \frac{127}{128} \)

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