
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 $y^{2}=2px (p > 0)$ that intersects with a line with a slope of $2\sqrt{2}$ at points $A(x_{1},y_{1}), B(x_{2},y_{2})$ $(x_{1} < x_{2})$ and the distance between $A$ and $B$ is $9$.

$(1)$ 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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