
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 problem is related to coordinate systems and parametric equations. In the rectangular coordinate system $xOy$, a pole is established at the coordinate origin, and the positive semi-axis of the $x$-axis is used as the polar axis to build a polar coordinate system. The polar coordinate equation of the curve $C1$ is $ρ\cos θ=4$.

(1) Point $M$ is a moving point on curve $C1$, and point $P$ is on line segment $OM$ such that $|OM|\cdot|OP|=16$. Determine the rectangular coordinate equation of the trajectory of point $P$ ($C2$).

(2) Let point $A$ have polar coordinates $\left(2, \dfrac{π}{3}\right)$, and point $B$ is on curve $C2$. Determine the maximum area of $\triangle OAB$.

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