
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 the line $l$: $x+y+a=0$ and the point $A(0,2)$, find the range of the real number $a$ such that there exists a point $M$ on line $l$ such that $|MA|^{2}+|MO|^{2}=10$, where $O$ is the origin.

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