
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 $xOy$, it is known that the ellipse $$C_{1}: \frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a>b>0)$$ has its left focus at $F_{1}(-1,0)$, and the minimum distance from a point on the ellipse to the focus is $\sqrt {2}-1$.
(1) Find the equation of the ellipse $C_{1}$;
(2) Suppose a line $l$ passes through the point $(0, \sqrt {2})$ and is tangent to the ellipse $C_{1}$, find the equation of line $l$.

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