
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 a linear pond with lily pads labeled from 0 to 8, a frog starts on pad 2. When the frog is on pad \( N \) where \( 0 < N < 8 \), it jumps two steps backward to pad \( N-2 \) (or to the nearest edge if \(N-2<0\)) with probability \( \frac{N}{8} \), and it jumps two steps forward to pad \( N+2 \) (or to the nearest edge if \(N+2>8\)) with the remaining probability. Find the probability that the frog will escape without being captured.

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