
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
Determine all values of the parameter \( p \) for which the system

$$
\left\{\begin{array}{l}
(x-p)^{2}=16(y-3+p) \\
y^{2}+\left(\frac{x-3}{|x|-3}\right)^{2}=1
\end{array}\right.
$$

has solutions and solve it for each of the found values of \( p \).

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