
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
Let \((1+\sqrt{2}+\sqrt{3})^{n}=p_n+q_n \sqrt{2}+r_n \sqrt{3}+s_n \sqrt{6}(n \geqslant 0)\). Find:
a) \(\lim_{{n \to \infty}} \frac{p_n}{q_n}\)
b) \(\lim_{{n \to \infty}} \frac{p_n}{r_n}\)
c) \(\lim_{{n \to \infty}} \frac{p_n}{s_n}\).

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