
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 curve $C_{1}$: $y^{2}=px$ $(y > 0, p > 0)$, and the tangent line at point $M(\frac{4}{p},2)$ of this curve is also tangent to the curve $C_{2}$: $y=e^{x+1}-1$. Find the value of $\frac{1}{2}p\ln\frac{{4{e^2}}}{p}$.

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