
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 park, there are nineteen lily pads arranged in a line labeled from 0 through 18. A frog starts on pad 3. When the frog is on pad \(N\), \(0 < N < 18\), it will jump to pad \(N-1\) with probability \( \frac{N}{18} \) and to pad \(N+1\) with probability \(1 - \frac{N}{18}\). If the frog reaches pad 0, it will hide in a burrow and be safe. If the frog reaches pad 18, it will escape the park. What is the probability that the frog reaches pad 18 without going to pad 0?
A) \( \frac{1361}{2187} \)
B) \( \frac{1093}{2187} \)
C) \( \frac{364}{729} \)
D) \( \frac{2}{3} \)
E) \( \frac{1}{2} \)

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