
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
There are four statements given below:

1. If the graph of the function $f(x) = a \sin x + \cos x (x \in \mathbb{R})$ is symmetrical about the line $x = \frac{\pi}{6}$, then $a = \frac{\sqrt{3}}{3}$;
2. Given vectors $\overrightarrow{a} = (1, 2)$ and $\overrightarrow{b} = (-2, m)$, if the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is obtuse, then $m < 1$;
3. When $\frac{5 \pi}{2} < \alpha < \frac{9 \pi}{2}$, the function $f(x) = \sin x - \log_a x$ has three zero points;
4. The function $f(x) = x \sin x$ is monotonically decreasing on $\left[- \frac{\pi}{2}, 0 \right]$ and monotonically increasing on $\left[0, \frac{\pi}{2} \right]$.

Determine the correct statement(s) by filling in the number(s) of all correct statements.

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