
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 polar coordinate system, randomly select two curves from the four curves $C\_1$: $ρ=1$, $C\_2$: $θ= \frac {π}{3}(ρ>=0)$, $C\_3$: $ρ=\cos θ$, $C\_4$: $ρ\sin θ=1$. Let the number of intersection points of these two curves be the random variable $ξ$. Find the mathematical expectation $Eξ=$ \_\_\_\_\_\_.

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