
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 $\Delta ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given the equation $1+\frac{\tan A}{\tan B} = \frac{2c}{\sqrt{3}b}$.

(1) Find the measure of angle $A$;
(2) If $\Delta ABC$ is an acute triangle, find the range of the function $y = 2\sin^2 B - 2\sin B \cos C$;
(3) Now, three conditions are given: $①a=1$; $②2c-(\sqrt{3}+1)b=0$; $③B=45^{\circ}$. Choose two of these conditions to determine $\Delta ABC$, and calculate the area of the determined $\Delta ABC$.

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