
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
Let the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ ($a<0$, $b<0$, $a \neq b$) have one common root. Let the other two roots be $x_1$ and $x_2$.

(1) Find the value of $x_1+x_2$.

(2) Find the maximum value of $x_1x_2$.

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