
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 the complex numbers $z\_1$ and $z\_2$ are symmetric about the real axis in the complex plane, and $z\_1=2+i$, find $z\_1z\_2=\_\_\_\_\_\_\_\_\_\_.$

(2) If the vertex of a parabola is at the origin, the axis of symmetry is the $y$-axis, and it passes through the point $(2,2)$, find the standard equation of the parabola.

(3) If the asymptotes of the hyperbola $\frac{x^2}{6}-\frac{y^2}{3}=1$ are tangent to the circle $(x-a)^2+y^2=3$, find $a=\_\_\_\_\_\_\_\_.$

(4) If the function $f(x)=2x+\frac{1}{2}\sin x$, and for any $x\in[-2,2], f(mx-3)+f(x)<0$ always holds, find the range of values for $m$.

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