
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
Given the function $g(x)=x-1$, and the function $f(x)$ satisfies $f(x+1)=-2f(x)-1$. When $x \in (0,1]$, $f(x)=x^{2}-x$. For any $x_1 \in (1,2]$ and $x_2 \in R$, determine the minimum value of $(x_1-x_2)^2+(f(x_1)-g(x_2))^2$.

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