
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 $$f(x)= \begin{cases} x^{2}+(a+b)x+2, & x\leq0 \\ 2, & x>0\end{cases}$$, where $a$ is a solution of the equation $x+\log x=4$, and $b$ is a solution of the equation $x+10^{x}=4$. If the equation $f(x)=x$ has solutions $x_{1}, x_{2}, \ldots, x_{n}$, and let $$\sum\limits_{i=1}^{n}x_{i}=x_{1}+x_{2}+\ldots+x_{n}$$, then $$\sum\limits_{i=1}^{n}x_{i}$$ equals \_\_\_\_\_\_.

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