
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 an acute triangle $ABC$ with angles $A$, $B$, $C$ and opposite sides $a$, $b$, $c$ respectively, it is known that $\sqrt{\frac{1 - \cos{2C}}{2}} + \sin(B - A) = 2\sin{2A}$.
(Ⅰ) Find the value of $\frac{a}{b}$.
(Ⅱ) If $AB$ is the longest side, determine the range of values for $\cos{C}$.

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