
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 the ellipse $C$: $\frac{x^{2}}{4} + \frac{y^{2}}{b} = 1$ and the line $l$: $y = mx + 1$, if for any $m \in \mathbb{R}$, the line $l$ always intersects with the ellipse $C$, then the range of the real number $b$ is _____.

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