
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
(1) Write the parametric equation of curve C, which is obtained by translating the circle $x^2 + y^2 - 2x = 0$ one unit to the left, and then multiplying the abscissa of each point on the resulting curve by $\sqrt{3}$ while keeping the ordinate unchanged.
(2) Given that line l has the polar equation $ρ \sin(θ + \frac{π}{4}) = \frac{3\sqrt{2}}{2}$, find the minimum value of the distance $|AB|$, where A and B are moving points on curve C and line l, respectively.

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