
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
A circle is defined by the equation $(x-1)^2 + y^2 = 1$. Move the circle one unit to the left to obtain a new curve. Then, for each point on the new curve, keep the y-coordinate the same and multiply the x-coordinate by $\sqrt{3}$ to obtain a new curve C.
(1) Write the parametric equation of curve C.
(2) In a polar coordinate system with the origin as the pole and the non-negative half of the x-axis as the polar axis, the polar equation of line l is given by $ρ \sin⁡(θ+π/4)=3\sqrt{2}/2$. If A and B are moving points on curve C and line l respectively, find the minimum value of |AB|.

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