
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 that the right focus of the ellipse $\dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ is $F(1,0)$, $M$ is the upper vertex of the ellipse, $O$ is the coordinate origin, and $\triangle OMF$ is an isosceles right-angled triangle.
(I) Find the equation of the ellipse;
(II) Does there exist a line $l$ that intersects the ellipse at points $P$ and $Q$ such that $F$ is the orthocenter of $\triangle PQM$ (i.e., the intersection point of the three altitudes)? If it exists, find the equation of line $l$; if not, explain the reason.

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