
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
For any real number, the line $y=x+b$ always has a common point with the ellipse $\begin{cases}x=2\cos \theta \\\\ y=4\sin \theta\end{cases}\left(0\leqslant \theta\leqslant \pi \right)$. Determine the range of values for $b$.

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