
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 coordinates of point $Q$, which is symmetric to point $P(2,1)$ with respect to the line $x-y+1=0$, are ______________.

(2) Given $\triangle ABC$ has an internal angle of $120^{\circ}$, and the lengths of its three sides form an arithmetic sequence with a common difference of $2$, the area of $\triangle ABC$ is ______________.

(3) Given $\{a_n\}$ is a geometric sequence with a common ratio $q$, and $S_n$ is the sum of the first $n$ terms of $\{a_n\}$, and $9S_3=S_6$, if positive numbers $a,b$ satisfy: $\frac{2}{a}+\frac{4}{b}=q$, then the minimum value of $\frac{2}{a-1}+\frac{1}{b-2}$ is ______________.

(4) Given the function $f(x)=\ln \frac{1+x}{1-x}+\sin x$, then the solution set of the inequality $f(a-2)+f(a^2-4) < 0$ is ______________.

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