
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
In the Cartesian coordinate system $xOy$, the parametric equation of curve $C_1$ is $$\begin{cases} x=4t^{2} \\ y=4t \end{cases}$$ (where $t$ is the parameter). Taking the origin $O$ as the pole and the positive $x$-axis as the polar axis, and using the same unit length, the polar equation of curve $C_2$ is $$ρ\cos(θ+ \frac {π}{4})= \frac { \sqrt {2}}{2}$$.
(Ⅰ) Convert the equation of curve $C_1$ into a standard equation, and the equation of curve $C_2$ into a Cartesian coordinate equation;
(Ⅱ) If curves $C_1$ and $C_2$ intersect at points $A$ and $B$, and the midpoint of $AB$ is $P$, and a perpendicular line to curve $C_2$ at point $P$ intersects curve $C_1$ at points $E$ and $F$, find $|PE|•|PF|$.

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