
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 a function $f(x)=a\sin x+b\cos x$ where $x\in \mathbb{R}$ and $\frac{b}{a} \in (1,\sqrt{3}]$. If the function $f(x)$ attains its maximum value at $x=x_{0}$, then the range of $\tan 2x_{0}$ is ______.

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