
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 plane rectangular coordinate system, two points $A(0, a)$ and $B(0, b)$ are given on the positive half of the $y$-axis, where $a > b > 0$. $C$ is a point on the positive half of the $x$-axis, and $\angle ACB$ is maximized. Find the coordinates of point $C$.

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