
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 values of \(a\) and \(b\) do the equations

\[ 
19 x^{2} + 19 y^{2} + a x + b y + 98 = 0 
\]

and 

\[ 
98 x^{2} + 98 y^{2} + a x + b y + 19 = 0 
\]

have a common solution?

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