
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 circle with equation (x - h)^2 + (y - k)^2 = r^2 passes through the points O(0,0), A(1,1), and B(4,2). The circle intersects the x-axis and y-axis at points S and T respectively (excluding the origin). Find the length |ST|.

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