
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
Definition: The solution sets of two inequalities about $x$, $f(x) < 0$ and $g(x) < 0$, are $(a, b)$ and $(\frac{1}{b}, \frac{1}{a})$, respectively. These two inequalities are called dual inequalities. If the inequality $x^{2}-4 \sqrt {3}x\cos 2θ+2 < 0$ and the inequality $2x^{2}+4x\sin 2θ+1 < 0$ are dual inequalities, and $θ∈(0,π)$, then $θ=$ _____ .

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