
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 a triangle $ABC$ with sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$, respectively, and an area $S$. It is known that $3a^{2}-4\sqrt{3}S=3b^{2}+3c^{2}$.
$(1)$ Find the measure of angle $A$.
$(2)$ If $a=3$, determine the range of possible values for the perimeter of $\triangle ABC$.

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