
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
Given the plane rectangular coordinate system $(xOy)$, point $P(x, y)$ moves on the curve $C$: $ \begin{cases}x=1+\cos θ \ y=\sin θ\end{cases} (θ$ is a parameter, $θ∈R$). Establish a polar coordinate system with $Ox$ as the polar axis. The polar coordinate equation of line $l$ is $ρ\cos (θ+ \frac {π}{4})=0$.
(I) Write the standard equation of curve $C$ and the rectangular coordinate equation of line $l$;
(II) If line $l$ intersects curve $C$ at points $A$ and $B$, and point $M$ moves on curve $C$, find the maximum value of $△ABM$'s area.

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