
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
Given that $a$, $b$, and $c$ are the sides opposite to the three internal angles of an acute triangle ($\Delta ABC$), and $b^{2}=a^{2}+c^{2}-ac$,

(1) If $\angle A=60^{\circ}$, $c=2$, then $a=$ _________

(2) If the area of ($\Delta ABC$) is $S=2\sqrt{3}$, then the range of the triangle's perimeter is _________

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