
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 $C: \frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1 (a>b>0)$ with its right focus $F(\sqrt {6},0)$, a line parallel to the y-axis passing through point F intersects the ellipse C, resulting in a chord length of $\sqrt {2}$.
(1) Find the standard equation of the ellipse;
(2) A line $l$ passing through the point $(1,0)$ intersects the ellipse $C$ at points $P$ and $Q$. Point $N$ is on the line $x=-1$. If $\triangle NPQ$ is an equilateral triangle, find the equation of line $l$.

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