
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
Let the function \( f(x) \) for any real number \( x \) satisfy: \( f(2-x) = f(2+x) \) and \( f(7-x) = f(7+x) \), and \( f(0) = 0 \). Let \( M \) be the number of roots of \( f(x) = 0 \) in the interval \([-1000, 1000]\). Find the minimum value of \( M \).

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