
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
Let the function $f(x)=x^{2}-1$. For any $x\in\left[\frac{3}{2},+\infty\right)$, the inequality $f\left(\frac{x}{\sin \theta}\right)-(4\sin^{2}\theta)f(x)\leqslant f(x-1)+4f(\sin \theta)$ always holds if $\theta\in(0,\pi)$. Find the range of $\theta$.

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