
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
In $\triangle ABC$, it is known that the internal angle $A= \frac{\pi}{3}$, side $BC=2\sqrt{3}$. Let internal angle $B=x$, and the area be $y$.
(1) If $x=\frac{\pi}{4}$, find the length of side $AC$;
(2) Find the maximum value of $y$.

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