
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
Find the derivative of the implicit function $y$ given by the equations: 

1) $x^{2} + y^{2} + 2x - 6y + 2 = 0$ 

2) $x^{y} = y^{x}$

and calculate its value at $x = 1$.

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