
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
Circles  $C_1$  and  $C_2$  intersect at points  $X$  and  $Y$  . Point  $A$  is a point on  $C_1$  such that the tangent line with respect to  $C_1$  passing through  $A$  intersects  $C_2$  at  $B$  and  $C$ , with  $A$  closer to  $B$  than  $C$ , such that  $2016 \cdot AB = BC$ . Line  $XY$  intersects line  $AC$  at  $D$ . If circles  $C_1$  and  $C_2$  have radii of  $20$  and  $16$ , respectively, find  $\sqrt{1+BC/BD}$ .

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