
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 reflective pond, there are twenty-one lilypads in a row labeled from 0 to 20. A frog sits on pad 3. When the frog is on pad $N$, where $0 < N < 20$, it will jump to pad $N - 1$ with probability $\frac{2N}{20}$ and to pad $N + 1$ with probability $1 - \frac{2N}{20}$. Each jump is independent of previous ones. If the frog reaches pad 0, it is eaten by a lurking snake. If the frog reaches pad 20, it escapes the pond forever. Calculate the probability that the frog escapes without being eaten.
**A)** $\frac{4}{11}$  
**B)** $\frac{10}{21}$  
**C)** $\frac{2}{5}$  
**D)** $\frac{5}{12}$  
**E)** $\frac{1}{3}$

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