
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
Given that the function $f(x)$ has a unique zero point that lies within the intervals $(0, 16)$, $(0, 8)$, $(0, 4)$, and $(0, 2)$, consider the following statements:
1. The function $f(x)$ has a zero point within the interval $(0,1)$.
2. The function $f(x)$ has a zero point within the interval $(0,1)$ or $(1,2)$.
3. The function $f(x)$ has no zero points within the interval $[2, 16)$.
4. The function $f(x)$ is either monotonically increasing or decreasing on the interval $(0,16)$.

Identify the correct statements. (List all correct statement numbers).

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