
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
Given that there are lily pads in a row numbered $0$ to $14$, and there are predators on lily pads $4$ and $8$, and a morsel of food on lily pad $13$, Fiona the frog starts on pad $0$, and from any given lily pad she has a $\frac{1}{3}$ chance to hop to the next pad, a $\frac{1}{3}$ chance to jump $2$ pads forward, and a $\frac{1}{3}$ chance to jump backward by $1$ pad, determine the probability that Fiona reaches pad $13$ without landing on either pad $4$ or pad $8$.

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