
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 ellipse $C_{1}$: $\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1(a > b > 0)$ has an eccentricity of $\dfrac{\sqrt{2}}{2}$, and the minimum distance from a point on the ellipse to the left focus of ellipse $C_{1}$ is $\sqrt{2}-1$.

(Ⅰ) Find the equation of $C_{1}$;

(Ⅱ) Suppose the line $l$ is tangent to both the ellipse $C_{1}$ and the parabola $C_{2}$: $y^{2}=4x$, find the equation of the line $l$.

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