
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
In the Cartesian coordinate system $xOy$, the line $l_{1}: 4x + 5y = 20$ intersects the $x$-axis and $y$-axis at points $A$ and $B$, respectively. Line $l_{2}$ intersects segments $AB$ and $OA$ at points $C$ and $D$, respectively, and it bisects the area of $\triangle AOB$. Find the minimum value of $CD^2$. ______

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