
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 from $0$ to $15$. There are predators on lily pads $4$ and $9$, and a morsel of food on lily pad $14$. Fiona the frog starts on pad $0$. At each lily pad, she has a $\frac{1}{2}$ chance to hop to the next pad, and an equal chance to jump $2$ pads, but she has an additional choice at pad $1$ where she can jump back to pad $0$ with a $\frac{1}{4}$ chance. What is the probability that Fiona reaches pad $14$ without landing on either pad $4$ or pad $9$?
**A) $\frac{3}{256}$**
**B) $\frac{3}{128}$**
**C) $\frac{3}{64}$**
**D) $\frac{1}{16}$**
**E) $\frac{1}{8}$**

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