
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
What is the relationship between \( A \) and \( p \), if

$$
A=\frac{x^{2}-3 y^{2}}{3 x^{2}+y^{2}}
$$

and

$$
\frac{p x y}{x^{2}-(2+p) x y+2 p y^{2}}-\frac{y}{x-2 y}=\frac{1}{2} ?
$$

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