
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
Friedrich the frog starts on a randomly determined square of a $4 \times 4$ grid, where he has different probabilities of choosing his next hop direction: up (30%), down (30%), left (20%), and right (20%). If a hop direction would take Friedrich off the edge of the grid, he moves to the diagonal opposite square instead of wrapping around. Special squares are at each of the four corners and the center. Friedrich will continue hopping for at most four hops or will stop if he lands on any of these special squares. What is the probability that Friedrich stops hopping by landing on one of the special squares within four hops?
- **A)** $\frac{1}{3}$
- **B)** $\frac{15}{64}$
- **C)** $\frac{29}{64}$
- **D)** $\frac{37}{64}$
- **E)** $\frac{53}{64}$

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