
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 a parabola $C: y^2 = 2px$ with the focus $F(1,0)$, and a line $L$ passing through $F$ intersects the parabola $C$ at points $A$ and $B$, the lines $AO$ and $BO$ intersect with the line $m: x=-2$ at points $M$ and $N$, respectively.  
(1) Find the equation of the parabola $C$.  
(2) Calculate the value of $\frac {S_{\triangle ABO}}{S_{\triangle MNO}}$.

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