
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 $E: y^{2}=4x$ with focus $F$ as the right focus of the ellipse $M: \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$. The two curves intersect at point $P$ in the first quadrant, and $|PF|= \frac{5}{3}$.

(Ⅰ) Find the equation of the ellipse $M$;

(Ⅱ) Through point $F$ and perpendicular to each other, two lines $l_{1}$ and $l_{2}$ intersect the ellipse $M$ at points $A$ and $B$, and the parabola $E$ at points $C$ and $D$, respectively, with $|CD|=4|AB|$. Find the equation of the line $l_{1}$.

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