
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 $C$ is $y^{2}=6x$:
(1) Find its focal coordinates and the equation of the directrix;
(2) Line $l$ passes through the known focus of the parabola $C$ with a slope angle of $45^{\circ}$, and intersects the parabola at points $A$ and $B$. Find the length of the line segment $AB$.

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