
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
In a row of 15 lily pads labeled 0 through 14, a frog starts on pad 3. When on pad $N$, where $0 < N < 14$, the frog jumps to pad $N-1$ with probability $\frac{N}{14}$ and to pad $N+1$ with probability $1-\frac{N}{14}$. Each jump is independent of previous jumps. If the frog reaches pad 0, it is captured by a hungry heron. If the frog reaches pad 14, it safely escapes. Find the probability of the frog escaping without being captured.
A) $\frac{357}{500}$
B) $\frac{1}{3}$
C) $\frac{21}{31}$
D) $\frac{12}{14}$
E) $\frac{4}{5}$

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