
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 that $f(x)$ is an odd function defined on $\mathbb{R}$, and $f(x)=2{x}^{2}-x$ when $x\leqslant 0$, find the value of $f(1)$.

(2) Find the equation of the tangent line to the curve of the function $f(x)= \frac{\ln x-2x}{x}$ at the point $(1,-2)$.

(3) Given that $f(x)$ is an odd function defined on $(-1,1)$ and is a decreasing function on its domain. If $f(m-2)>f(-2m+3)$, find the range of values for the real number $m$.

(4) Given the function $f(x)=\begin{cases}{x}^{2}+ \frac{1}{2}a-2,x\leqslant 1 \\ {a}^{x}-a,x > 1\end{cases}$, find the range of values for the real number $a$ such that $f(x)$ is increasing on $(0,+\infty)$.

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