
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
Let $M(x_0,y_0)$ be a point on the parabola $y^2 = 8x$, and let $F$ be the focus of the parabola. If a circle with $F$ as its center and $|FM|$ as its radius intersects the directrix of the parabola, determine the range of values for $x_0$.

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