
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
A wishing well is located at the point  $(11,11)$  in the  $xy$ -plane. Rachelle randomly selects an integer  $y$  from the set  $\left\{ 0, 1, \dots, 10 \right\}$ .  Then she randomly selects, with replacement, two integers  $a,b$  from the set  $\left\{ 1,2,\dots,10 \right\}$ .  The probability the line through  $(0,y)$  and  $(a,b)$  passes through the well can be expressed as  $\frac mn$ , where  $m$  and  $n$  are relatively prime positive integers.  Compute  $m+n$ .

*Proposed by Evan Chen*

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