
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 \( g(5+x) = g(5-x) \) and \( g(9+x) = g(9-x) \) for all \( x \). If \( g(0) = 0 \), what is the least 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}
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