
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 \(\frac{x^{2}}{2} + y^{2} = 1\), with \(DA \perp AB\), \(CB \perp AB\), \(DA = 3\sqrt{2}\), and \(CB = \sqrt{2}\), find the minimum area of \(\triangle PCD\) where point \(P\) moves along the arc \(AB\).

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