
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
A salmon swimming along a mountain stream must pass two waterfalls. In this experiment, the probability of the salmon passing the first waterfall is \( p > 0 \), and the probability of passing the second waterfall is \( q > 0 \). Assuming the trials of passing each waterfall are independent, find the probability that in \( n \) trials, the salmon fails to pass the first waterfall given that it fails to pass both waterfalls.

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