
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 $C: \frac{x^{2}}{2}+y^{2}=1$ and the line $l: y=x-1$, which intersect at points A and B. Find the equation of the circle that passes through points A and B and is tangent to the line $m: x= \frac{4}{3}$.

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