
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
(1) The graph of the function $y=\log_{a}(x-2)+3$ $(a > 0, a \neq 1)$ always passes through a certain point ______.

(2) In the polar coordinate system, if the polar coordinates of points $A$ and $B$ are $(3, \frac{\pi}{3})$ and $(-4, \frac{7\pi}{6})$, respectively, then the area of $\triangle AOB$ ($O$ is the pole) is equal to ______.

(3) The solution set of the inequality $|x+2|+|x-1| \leqslant 4$ is ______.

(4) Given that $f(x)$ is an odd function defined on $\mathbb{R}$, and when $x > 0$, $f(x)$ is a power function, and its graph passes through the point $(3, \sqrt{3})$, then the expression of $f(x)$ on $\mathbb{R}$ is ______.

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