
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 the real parameter  $p$  be such that the system  $\begin{cases} p(x^2 - y^2) = (p^2- 1)xy  |x - 1|+ |y| = 1 \end{cases}$  has at least three different real solutions. Find  $p$  and solve the system for that  $p$ .

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