
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) In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $A=60^{\circ}$, $b=1$, and the area of $\triangle ABC$ is $\sqrt{3}$, then $a=$       .

(2) The sum of the first $n$ terms of the sequence $\{a_n\}$ is $S_n=3n^2-2n$. Then, the general term formula of the sequence $a_n=$       .

(3) Given that the sum of the first $n$ terms of a geometric sequence $\{a_n\}$ is $48$, and the sum of the first $2n$ terms is $60$, then the sum of the first $3n$ terms is     .

(4) In an obtuse $\triangle ABC$, where $a=1$, $b=2$, the range of the maximum side $c$ is        .

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