
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 that the domain of the function $y=f(x)$ is $R$, if there exists a constant $M_0$ such that $|f(x)|\geqslant M|x|$ holds for all real numbers $x$, then $f(x)$ is called a "cone-bottomed" function. If $f(x)=x^2+1$ is a "cone-bottomed" function, find the maximum value of $M$.

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