
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 $ABC$, the sides opposite angles A, B, and C are $a, b,$ and $c$ respectively. Given that $\angle A = \frac{\pi}{6}$ and $a=2$; let the internal angle at B be $x$, and the area of the triangle $ABC$ be $y$.
(1) Find the expression and domain of function $y = f(x)$;
(2) Find the range of function $y = f(x)$.

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