
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 \( p(x) \) be the polynomial of degree 4 with roots 1, 2, 3, and 4, and leading coefficient 1. Let \( q(x) \) be the polynomial of degree 4 with roots 1, \(\frac{1}{2}\), \(\frac{1}{3}\), and \(\frac{1}{4}\), and leading coefficient 1. Find \(\lim_{x \rightarrow 1} \frac{p(x)}{q(x)}\).

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