
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 $y^2 = 8x$ with focus $F$, a line passing through $F$ at an angle of $60^\circ$ intersects the parabola at points $A$ and $B$ (with point $A$ in the first quadrant), and intersects its directrix at point $C$. Calculate the ratio of the areas of triangles $AOC$ and $BOF$, which is $\frac {S_{△AOC}}{S_{△BOF}}$.

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