
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 that the domain of the function $y=f(x)$ is $\mathbb{R}$, and the function $g(x)=f(x+5)+f(1-x)$. If the equation $g(x)=0$ has exactly 7 different real solutions, then the sum of these 7 real solutions is \_\_\_\_\_\_.

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