
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
There are lily pads in a row numbered $0$ to $15$, in that order. There are predators on lily pads $4$ and $9$, and a morsel of food on lily pad $13$. Fiona the frog begins her journey on pad $0$, and from any given lily pad, she has a probability of $\frac{1}{2}$ to either hop to the next pad or jump two pads forward. Determine the probability that Fiona reaches pad $13$ without landing on either pad $4$ or $9$.
**A) $\frac{9}{1024}$  
B) $\frac{27}{1024}$  
C) $\frac{13}{512}$  
D) $\frac{64}{512}$  
E) $\frac{15}{256}$**

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