
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 rectangular coordinate system $xOy$, the parametric equations of the curve $C_1$ are given by: $$\begin{cases}x=2+2\cos α \\ y=4+2\sin α\end{cases}$$ (where $α$ is the parameter). Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar equation of the line $C_2$ is $θ= \frac {π}{4}$ (where $ρ∈R$).

1. Find the polar equation of $C_1$.
2. If the line $C_2$ intersects the curve $C_1$ at points $M$ and $N$, find $|MN|$.

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