
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 $P$ is a point on the ellipse $\frac{y^{2}}{8} + \frac{x^{2}}{2} = 1$, $A$ and $B$ are the upper and lower vertices of the ellipse, respectively. The lines $PA$ and $PB$ intersect with the line $x = -2$ at points $C$ and $D$, respectively. $O$ is the coordinate origin. Find the minimum area of $\triangle OCD$.

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