
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
Given the parabola $y^2 = 4x$ with focus $F$, a line $l$ passing through the point $(a, 0)$ ($a < 0$) at an angle of $\frac{\pi}{6}$ intersects the parabola at points $C$ and $D$. If $F$ is outside the circle with diameter $CD$, find the range of values for $a$.

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