
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 that $θ∈[0, \frac{π}{2}]$, the chord length formed by the intersection of the line $x\sin θ+y\cos θ-1=0$ and the circle $C$: $(x-1)^{2}+(y-\cos θ)^{2}= \frac{1}{4}$ is $\frac{\sqrt{3}}{2}$. Determine the value of $θ$.

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