
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 \( n \in \mathbf{N}^{*} \), constants \( p \) and \( q \) both greater than 1 and not equal to 2, find the limit of \(\lim _{n \rightarrow \infty} \frac{p^{n+1}-q^{n}}{p^{n+2}-2 q^{n+1}}\).

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