
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 standard equation of the parabola is $y^2=6x$,

(I) Find the coordinates of the focus and the equation of the directrix;
(II) Line $L$ passes through the known focus of the parabola and has a slope angle of $45^{\circ}$, and the intersection points of the line $L$ and the parabola are $A$ and $B$. Find the length of $AB$.

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