
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 line $l$ passes through the left focus $F$ of the ellipse $C$: $$\frac {x^{2}}{2}$$+y<sup>2</sup>\=1 and intersects the ellipse $C$ at points $A$ and $B$. $O$ is the coordinate origin. If $$\overrightarrow {OA}$$$$\cdot \overrightarrow {OB}$$\=0, draw a line perpendicular to $AB$ through point $O$, with $H$ as the foot of the perpendicular. Determine the coordinates of point $H$.

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