
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
Define  $f(x,y)=\frac{xy}{x^2+y^2\ln(x^2)^2}$  if  $x\ne0$ , and  $f(0,y)=0$  if  $y\ne0$ . Determine whether  $\lim_{(x,y)\to(0,0)}f(x,y)$  exists, and find its value is if the limit does exist.

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