
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, given an arbitrary angle $\theta$ with its initial side being the non-negative part of the x-axis, if the terminal side passes through the point $P(x_0, y_0)$, and $|OP|=r (r>0)$, define $sicos\theta=\frac {x_{0}+y_{0}}{r}$ and call "sicos$\theta$" the "positive cosine function." For the positive cosine function $y=sicosx$, a student derives the following conclusions:
1. The function is an even function;
2. A center of symmetry for the function is at $\left(\frac{3\pi}{4}, 0\right)$;
3. The function is monotonically decreasing within the intervals: $[2k\pi-\frac{3\pi}{4}, 2k\pi+\frac{\pi}{4}]$, where $k \in \mathbb{Z}$;
4. The graph of the function has no common points with the line $y=\frac{3}{2}$;
Among these conclusions, all the correct serial numbers are _______.

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