
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
A function $g$ is defined for all real numbers and satisfies $g(3+x)=g(3-x)$ and $g(8+x)=g(8-x)$ for all $x$. If $g(0) = 0$, what is the least number of roots $g(x)=0$ must have in the interval $-1500 \leq x \leq 1500$?

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