
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
Set up a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis. Given the curve $C_{1}: (x-2)^{2}+y^{2}=4$, the polar coordinates of point A are $(3\sqrt{2}, \frac{\pi}{4})$, and the polar equation of line l is $\rho\cos(\theta- \frac{\pi}{4})=a$, with point A lying on line l.
(1) Find the polar equation of curve $C_{1}$ and the Cartesian equation of line l.
(2) If line l is translated 6 units to the left to obtain line $l'$, and $l'$ intersects curve $C_{1}$ at points M and N, find the polar equation of $l'$ and the length of |MN|.

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