
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 $y^{2}=2px(p > 0)$ intersects with the line $y=2x-4$ at points $A$ and $B$. If there exists a point $C$ on the parabola such that $\overrightarrow{OA}+\overrightarrow{OB}= \frac{1}{5}\overrightarrow{OC}$ (where $O$ is the origin) and $M(2,2)$, calculate the product of the slopes of lines $AM$ and $BM$.

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