
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 function $g(x)$ satisfies $g(3+x)=g(3-x)$ for all real numbers $x$. If the equation $g(x)=0$ has exactly six distinct real roots, then the sum of these roots is
A) 12
B) 14
C) 16
D) 18
E) 20

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