
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 \( M = \left\{(x, y) \mid x^{2} + 2y^{2} = 3 \right\} \) and \( N = \{(x, y) \mid y = mx + b \} \), if for all \( m \in \mathbb{R} \), we have \( M \cap N \neq \varnothing \), then determine the range of values for \( b \).

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