
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 that the vertex of parabola $C$ is at the origin, symmetrical about the coordinate axis, and the equation of the directrix is $x=-1$.
(1) Determine the standard equation of the parabola $C$.
(2) A line $l$ passing through the focus of the parabola $C$ intersects the parabola at points $A$ and $B$. If the following conditions need to be satisfied: ① $|AB|\leq 8$; ② Line $l$ has intersection points with the ellipse $3x^2+2y^2=2$, determine the range of the slope angle $\alpha$ of the line $l$.

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