
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  $f$  is defined for all real numbers and satisfies \[f(2 + x) = f(2 - x)\qquad\text{and}\qquad f(7 + x) = f(7 - x)\] for all real  $x$ .  If  $x = 0$  is a root of  $f(x) = 0$ , what is the least number of roots  $f(x) = 0$  must have in the interval  $-1000 \le x \le 1000$ ?

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