
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
The polar coordinate equation of the curve is given by $ρ=\frac{2}{1-cos⁡θ}$. Two perpendicular lines passing through the origin intersect the curve at points $A$, $B$ and $C$, $D$ respectively. What is the value of the slope angle when $|AB|+|CD|$ reaches its minimum value? Also, find this minimum value.

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