
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
Define a function $g$ such that for all real numbers $x$, \( g(3+x)=g(3-x) \) and \( g(8+x)=g(8-x) \). If \( g(1) = 0 \), determine the minimum number of roots \( g(x) = 0 \) must have in the interval \(-1000 \leq x \leq 1000\).

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