
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 parametric equation of curve C1 is given by $$C_{1}:\begin{cases} x=2t+1 \\ y=2t-3 \end{cases}$$. Establish a polar coordinate system with the origin as the pole and the positive half of the x-axis as the polar axis using the same unit length. Curve C2: ρ=2acosθ (a>0) is symmetric about C1.
(I) Find the polar coordinate equation of C1 and the rectangular coordinate equation of C2;
(II) Translate C2 four units to the left to obtain C3, which is transformed according to $$\begin{cases} x'=x \\ y'=\frac{\sqrt{3}}{2}y \end{cases}$$. C3 intersects with both coordinate axes at points A and B. P is any point on C3. Find the maximum area of ΔABP.

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