
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 \( \triangle ABC \) with interior angles \( \angle A, \angle B, \angle C \) and opposite sides \( a, b, c \) respectively, with the relation \( 1 + \frac{\tan B}{\tan A} = \frac{2c}{\sqrt{3}a} \):

(1) Find \( \angle B \);

(2) If \( \triangle ABC \) is an acute triangle and \( a = 2 \), find the range of possible values for the area of \( \triangle ABC \).

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