
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 $y^2=2px$ ($p>0$) with focus, a line with slope $2\sqrt{2}$ intersects the parabola at points $A(x_1, y_1)$ and $B(x_2, y_2)$ ($x_1<x_2$), and $|AB|=18$.  
(1) Find the equation of this parabola;  
(2) Let $O$ be the origin, and $C$ be a point on the parabola. If $\overrightarrow{OC} = \overrightarrow{OA} + \lambda \overrightarrow{OB}$, find the value of $\lambda$.

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