
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 $\triangle ABC$, $a$, $b$, $c$ are the lengths of the sides opposite to angles $A$, $B$, $C$ respectively. Point $D$ lies on $BC$ such that $BD=2CD$ and $AD=2$.  
$(1)$ Choose one of the following conditions ① or ② as given information and find angle $A$.  
$(2)$ Under the condition chosen in $(1)$, find the maximum area of triangle $\triangle ABC$.  
Condition ①: ${\sin^2}B+{\sin^2}C=\sin A\left(\frac{2\sqrt{3}}{3}\sin B\sin C+\sin A\right)$;  
Condition ②: $\cos ^{2}A-\cos ^{2}B+\sin ^{2}C=\sin B\sin C$.  
Note: If both conditions ① and ② are solved separately, the first solution will be scored.

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