
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
The moving line $2ax+(a+c)y+2c=0$ ($a\in\mathbb{R}, c\in\mathbb{R}$) passes through a fixed point $(m,n)$, and $x_1+x_2+m+n=15$ with $x_1>x_2$. The minimum value of $$\frac{x_1^2+x_2^2}{x_1-x_2}$$ is \_\_\_\_\_\_.

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