
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 \( x \) and \( y \) be real numbers satisfying the equation \( (x - \sqrt{p})^2 + (y - \sqrt{p})^2 = 1 \). If \( k = \frac{y}{x - 3} \) and \( q \) is the least possible value of \( k^2 \), find the value of \( q \).

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