
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 a circle centered at $O$ with radius $r$, a tangent at point $A$ and a secant passing through point $A$ intersect the circle at points $C$ and $D$ such that $C$ is between $A$ and $D$. If the length of the tangent from $A$ to the point of tangency is $t$ and the segment $AC = s$, find the length of the segment $CD$.
A) $\frac{t^2 + s^2}{s}$
B) $\frac{t^2 - s^2}{s}$
C) $\frac{t+s}{s}$
D) $\frac{s^2 - t^2}{s}$
E) $\frac{t^2}{s - s^2}$

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