
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 intersect at the points  $C$  and  $D$ . The straight lines  $CD$  and  $BYXA$  intersect at the point  $Z$ . Moreever, the straight line  $WB$  is tangent to both of the circles. Suppose  $ZX=ZY$  and  $AB\cdot AX=100$ . Find the value of  $BW$ .

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