
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 $y^2=2px$ ($p>0$), a line passing through point $E(m, 0)$ ($m \neq 0$) intersects the parabola at points $M$ and $N$, and intersects the y-axis at point $P$. If $\overrightarrow{PM} = \lambda \overrightarrow{ME}$ and $\overrightarrow{PN} = \mu \overrightarrow{NE}$, calculate the value of $\lambda + \mu$.

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