
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
In the usual coordinate system  $ xOy$  a line  $ d$  intersect the circles  $ C_1:$   $ (x\plus{}1)^2\plus{}y^2\equal{}1$  and  $ C_2:$   $ (x\minus{}2)^2\plus{}y^2\equal{}4$  in the points  $ A,B,C$  and  $ D$  (in this order). It is known that  $ A\left(\minus{}\frac32,\frac{\sqrt3}2\right)$  and  $ \angle{BOC}\equal{}60^{\circ}$ . All the  $ Oy$  coordinates of these  $ 4$  points are positive. Find the slope of  $ d$ .

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