
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
Transform into polar coordinates \( x = r \cos \varphi, \quad y = r \sin \varphi \) the expression \( \frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}} \) (the Laplace operator in the plane), where \( u = u(x, y) \) is a twice differentiable function.

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