
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 parametric equation of line $l$ as $ \begin{cases} x=4- \frac { \sqrt {2}}{2}t \\ y= \frac { \sqrt {2}}{2}t \end{cases} (t \text{ is a parameter})$. Curve $C_{1} \begin{cases} x=1+\cos α \\ y=\sin α \end{cases} (α \text{ is a parameter})$. Curve $C_{2} \begin{cases} x=2+2\cos φ \\ y=2\sin φ \end{cases} (φ \text{ is a parameter})$. Establish a polar coordinate system with point $O$ as the origin and the positive semi-axis of $x$ as the polar axis.
(1) Find the polar coordinate equations of line $l$, curve $C_{1}$, and curve $C_{2}$;
(2) Ray $θ= \frac {π}{3}$ intersects with curve $C_{1}$ at points $O$ and $A$, and with curve $C_{2}$ at points $O$ and $B$. Ray $θ= \frac {2π}{3}$ intersects with line $l$ at point $C$. Calculate the area of $△CAB$.

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