
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
A line passing through point $A(-2,4)$ with a slope of $135^{\circ}$ intersects the parabola $y^{2}=2px$ ($p \gt 0$) at points $M$ and $N$. It is given that $\overrightarrow{AM}=\lambda \overrightarrow{MN}$ and $\overrightarrow{AN}=\frac{1}{\lambda}\overrightarrow{MN}$, where $\lambda \gt 0$. Find the values of $p$ and $\lambda$.

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