
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 C: $y^2$ = 8x. Let F be the focus of the parabola C. If a circle with F as the center and |FM| as the radius intersects the directrix of the parabola C, determine the range of values for $x_0$.

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