
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
Let  $ABCD$  be a convex quadrilateral.  $O$  is the intersection of  $AC$  and  $BD$ .  $AO=3$  , $BO=4$ ,  $CO=5$ ,  $DO=6$ .  $X$  and  $Y$  are points in segment  $AB$  and  $CD$  respectively, such that  $X,O,Y$  are collinear. The minimum of  $\frac{XB}{XA}+\frac{YC}{YD}$  can be written as  $\frac{a\sqrt{c}}{b}$  , where  $\frac{a}{b}$  is in lowest term and  $c$  is not divisible by any square number greater then  $1$ . What is the value of  $10a+b+c$ ?

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