
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
Circle  $\omega_1$  and  $\omega_2$  have centers  $(0,6)$  and  $(20,0)$ , respectively.  Both circles have radius  $30$ , and intersect at two points  $X$  and  $Y$ .  The line through  $X$  and  $Y$  can be written in the form  $y = mx+b$ .  Compute  $100m+b$ .

*Proposed by Evan Chen*

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