
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
The parabola $y=-\frac{1}{3}{x^2}+3$ intersects the negative half of the $x$-axis at point $A$ and the $y$-axis at point $B$. The parabola $G$ is translated along the line $AB$ to obtain the parabola $H$. If the parabola $H$ intersects the $y$-axis at point $D$, determine the maximum value of the ordinate of point $D$.

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