
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 \( f \) is defined on the set of real numbers and satisfies the equations \( f(2 - x) = f(2 + x) \) and \( f(7 - x) = f(7 + x) \) for all real numbers \( x \). Given that \( x = 0 \) is a root of \( f(x) = 0 \), let \( N \) be the number of roots of \( f(x) = 0 \) in the interval \([-1000, 1000]\). Find the minimum value of \( N \).

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