
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 the area of $\triangle ABC$ is $S$, and $\overrightarrow{AB} \cdot \overrightarrow{AC} = \frac{2\sqrt{3}}{3}S$.

1. Find the value of angle $A$.
2. If $\tan B = 2, |\overrightarrow{CA} - \overrightarrow{CB}| = 3$, find the area of $\triangle ABC$, denoted as $S$.
3. If the circumradius of $\triangle ABC$ is $1$, find the range of the area of $\triangle ABC$.

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