
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 lily pads in a row numbered from $0$ to $15$, with predators on pads $2$, $5$, and $8$, and a morsel of food on pad $14$, calculate the probability that Fiona the frog, starting on pad $0$, reaches pad $14$ without landing on either pad $2$, $5$, or $8$, given that from any given lily pad, Fiona has a $\frac{1}{2}$ chance to hop to the next pad, and an equal chance to jump $3$ pads.

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