
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
Two circles touch each other externally at point $K$. On their common internal tangent, a point $P$ is marked such that $K P = 14$. Through point $P$, two secants are drawn to the circles such that one of them cuts a chord $AB = 45$ on the first circle, and the other cuts a chord $CD = 21$ on the second circle, with point $A$ lying between points $B$ and $P$, and point $C$ lying between points $D$ and $P$. Find the ratio $BC: AD$.

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