
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]


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For any real number, if the line $y=x+b$ always has a common point with the ellipse parameterized as $\begin{cases} x=2\cos\theta \\ y=4\sin\theta \end{cases}$ $(0 \leq \theta < \pi)$, then the range of possible values for $b$ is ________.

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