
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
For which value of $\lambda$ is there a pair of values $x$ and $y$ that satisfies the following system of equations:

$$
x^{2}+y^{2}=8 x+6 y ; \quad 9 x^{2}+y^{2}=6 y ; \quad y^{2}+9=\lambda x+6 y+\lambda
$$

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