
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 $xOy$, the vertex of an angle coincides with the origin, and the initial side of the angle coincides with the non-negative half-axis of $x$. It is known that point $P(x, y)$ is a point on the terminal side of angle $\theta$, $|OP|=r$ ($r>0$), and define $f(\theta) = \frac{x-y}{r}$. For the following statements:
1. The range of function $f(\theta)$ is $[-\sqrt{2}, \sqrt{2}]$;
2. The graph of function $f(\theta)$ is symmetric about the origin;
3. The graph of function $f(\theta)$ is symmetric about the line $\theta= \frac{3\pi}{4}$;
4. Function $f(\theta)$ is a periodic function with the smallest positive period of $2\pi$;
5. The monotonically decreasing interval of function $f(\theta)$ is $[2k\pi- \frac{3\pi}{4}, 2k\pi+ \frac{\pi}{4}]$, where $k\in Z$.

The correct statements are \_\_\_\_\_\_ . (Fill in the serial numbers of all correct statements)

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