
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 $ABC$, let the sides opposite angles $A$, $B$, and $C$ be $a$, $b$, and $c$, respectively. Given that $a=4$, $B= \frac{\pi}{3}$, and the area of triangle $ABC$, $S_{\triangle ABC} = 6\sqrt{3}$, find the length of side $b$.

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