
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) Given the function $f(x)=\begin{cases}x^{2}-x, & (x\geqslant 0) \\ x+1, & (x < 0)\end{cases}$, then $f(2)=$ ______.

(2) Let $S_{n}$ be the sum of the first $n$ terms of an arithmetic sequence $\{a_{n}\}$, and $a_{3}=5$, $S_{6}=42$, then $S_{9}=$ ______.

(3) Let $\triangle ABC$ have sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$ respectively. If $\cos A= \frac{3}{5}$ and $\sin B= \frac{\sqrt{2}}{2}$ with $a=8$, then $c=$ ______.

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

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