
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 radius of circle $P$ is equal to the length of the major axis of the ellipse $\frac{x^2}{4} + \frac{y^2}{9} = 1$, and the center of the circle is the focus of the parabola $y^2 = 4\sqrt{2}x$, find the minimum value of the length of the minor arc of circle $P$ divided by line $l$ passing through the point $M(-\sqrt{2}, 1)$.

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