
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 $f(x) = \sin x \cos x + \sin^2 x - \frac{1}{2}$.

(i) Determine the smallest positive period and the maximum value of $f(x)$.
(ii) If $\alpha \in \left(0, \frac{\pi}{2}\right)$ and $f(\alpha) = \frac{\sqrt{2}}{2}$, find the value of $\alpha$.

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