
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)** Simplify $f(a)= \dfrac{\sin (\pi-a)\cdot\cos (2\pi-a)\sin \left( \dfrac{3\pi}{2}-a\right)}{\sin \left( \dfrac{\pi}{2}-a\right)\sin (\pi+a)} =$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

**(2)** Given that the function $f(x)$ is an odd function defined on $\mathbb{R}$, and when $x > 0$, $f(x)={3}^{-x}$. Then $f\left( -2+\log_{3}5 \right)=$\_\_\_\_\_\_\_\_\_\_．

**(3)** Given two lines $l_{1}:x+m^{2}y+2=0$, $l_{2}:(m-2)x+3my-6=0$. If $l_{1}$ is parallel to $l_{2}$, then $m=$\_\_\_\_\_\_\_\_

**(4)** The function $f(x)$ is defined on $[a,b]$. If for any $x_{1},x_{2}\in[a,b]$, it holds that $f\left(\dfrac{x_{1}+x_{2}}{2}\right) \leqslant \dfrac{1}{2}[f(x_{1})+f(x_{2})]$, then $f(x)$ is said to have property $P$ on $[a,b]$. Suppose $f(x)$ has property $P$ on $[1,3]$, the following statements are given:
- **(①)** The graph of $f(x)$ is continuous on $[1,3]$;
- **(②)** $f(x^{2})$ has property $P$ on $[1,\sqrt{3}]$;
- **(③)** If $f(x)$ attains its maximum value of $1$ at $x=2$, then $f(x)=1$ for $x\in[1,3]$;
- **(④)** For any $x_{1},x_{2},x_{3},x_{4}\in[1,3]$, it holds that $f\left(\dfrac{x_{1}+x_{2}+x_{3}+x_{4}}{4}\right) \leqslant \dfrac{1}{4}[f(x_{1})+f(x_{2})+f(x_{3})+f(x_{4})]$.
  
The correct sequence numbers are \_\_\_\_\_\_\_\_\_\_

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