
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 sets $M=\{(x,y)|x^{2}+2y^{2}=3\}$ and $N=\{(x,y)|y=mx+b\}$. If for all $m\in R$, there is always $M\cap N\neq \emptyset$, then determine the range of values for $b$.

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