
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
In the Cartesian coordinate system $xOy$, for any angle $\theta$ with the origin $O$ as the vertex and the positive half-axis of the $x$-axis as the initial side, if the terminal side passes through $P(x_0, y_0)$ and $|OP| = r$ ($r > 0$), define: $sos\theta = \frac{y_0 + x_0}{r}$, and call "$sos\theta$" the "sine cosine function". For the "sine cosine function" $y = sosx$, a student found the following properties:
1. The range of the function is $[-\sqrt{2}, \sqrt{2}]$;
2. The graph of the function is symmetric about the origin;
3. The graph of the function is symmetric about the line $x = \frac{3\pi}{4}$;
4. The function is periodic, with the smallest positive period being $2\pi$;
5. The function is monotonically increasing in the interval $[2k\pi - \frac{3\pi}{4}, 2k\pi + \frac{\pi}{4}]$, where $k \in \mathbb{Z}$

Among the above properties, the correct ones are \_\_\_\_\_\_ (fill in the serial numbers of all correct properties).

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