
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 $f(x)$ be defined on $(-\infty, +\infty)$ and satisfy the following conditions: $$f(x) = f(4-x),$$ $$f(7-x) = f(7+x),$$ and on the closed interval $[0, 7]$ only $f(1)=f(3)=0$. Determine the smallest positive period of the function $f(x)$ and the number of roots of the equation $f(x)=0$ in the closed interval $[-2005, 2005]$.

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