
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 $xOy$, if the line $l: x+2y=0$ is tangent to the circle $C: (x-a)^{2}+(y-b)^{2}=5$, and the center of the circle $C$ is above the line $l$, then the maximum value of $ab$ is \_\_\_\_\_\_.

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