
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 $f(x) = \cos(2x + \frac{\pi}{3}) + \sin^2{x}$,  
(Ⅰ) Find the maximum value of $f(x)$ and its smallest positive period;  
(Ⅱ) For triangle $ABC$ with angles $A$, $B$, $C$, if $\cos{B} = \frac{1}{3}$ and $f\left(\frac{C}{2}\right) = -\frac{1}{4}$ with $C$ being an acute angle, find $\sin{A}$.

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