
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
Denote the circles around $A$ and $B$ in problem 1448 by $k_{1}$ and $k_{2}$, respectively, with radii $r_{1}$ and $r_{2}$. Let $k$ be a circle that is tangent to $k_{1}$ and $k_{2}$ from the inside, with radius $r_{3}$. What does the ratio $r_{3} / r_{1}$ approach when, fixing $A$ and $B$, the point $C$ approaches $A$, i.e., as $r_{1}$ approaches 0?

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