
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 distance between points P and Q is minimized when they are closest to each other on curves C1 and C2, respectively. Find the minimum value of |PQ|, where P and Q are points on curves $C_1$ and $C_2$ given by the equations $\begin{cases}x= \sqrt {2}\cos α \\ y=1+ \sqrt {2}\sin α\end{cases}$ and $\sqrt {2}ρ\sin (θ+ \dfrac {π}{4})=5$.

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