
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 $f(x)=2\sin x\cos^2\left(\dfrac{θ}{2}\right)+\cos x\sin θ-\sin x(0 < θ < π)$, find the minimum value at $x=π$.

(I) Find the value of $θ$;

(II) In $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively. Given $a=1$, $b= \sqrt{2}$, $f(A)=\dfrac{ \sqrt{3}}{2}$, find angle $C$.

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