
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
In the Cartesian coordinate system $xOy$, given a circle $C: (x+1)^2 + y^2 = 2$ and a point $A(2,0)$. If there exists a point $M$ on circle $C$ such that $MA^2 + MO^2 \leqslant 10$, then the range of the $y$-coordinate of point $M$ is __________.

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