
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
For the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a > b > 0)$, if the projection of one of its foci $F$ onto a line $l$ is $H$, then the necessary and sufficient condition for the line $l$ to be tangent to (intersect, be disjoint from) the ellipse is that point $H$ lies on (inside, outside) the circle $x^{2}+y^{2}=a^{2}$.

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