
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 the function $f(x) = \sin(2x + \frac{\pi}{6})$,  
(Ⅰ) If $f(\alpha) = \frac{2}{3}$, find the value of $f(\alpha - \frac{\pi}{12})$;  
(Ⅱ) In triangle $ABC$, if $f(A) = \frac{\sqrt{3}}{2}$, $\angle B = \frac{\pi}{4}$, and $AC = 2$, find the area of triangle $ABC$.

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