
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 $xOy$, it is known that the line $l: x + y + a = 0$ and point $A(2,0)$ are given. If there exists a point $M$ on line $l$ such that $|MA| = 2|MO|$ (where $O$ is the origin), find the range of values for the real number $a$.

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