
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 $f(x)=\frac{1}{2}\sin\left(ωx+φ\right)\ (ω > 0, 0 < φ < π)$ is an even function, points $P, Q$ are adjacent highest and lowest points on the graph of $y = f(x)$, and $|PQ| = \sqrt{2}$.

(I) Find the analytical expression of the function $f(x)$;

(II) In $∆ABC$, $a, b, c$ are the sides opposite to angles $A, B, C$ respectively. Given $a = 1$, $b = \sqrt{2}$, and $f(\frac{A}{π}) = \frac{\sqrt{3}}{4}$, find the measure of angle $C$.

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