
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 Cartesian coordinate system $(xOy)$, establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. Given that in the polar coordinate system, $A(3 \sqrt {3}, \frac {π}{2})$, $B(3, \frac {π}{3})$, and the equation of circle $C$ is $ρ=2\cos θ$.
(1) Find the standard equation of circle $C$ in the Cartesian coordinate system;
(2) Given that $P$ is any point on circle $C$, find the maximum value of the area of $\triangle ABP$.

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