
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 curve C is $\begin{cases}x=\cos \theta \\\ y=\sin \theta\end{cases}(\theta \text{ is the parameter})$, establish a polar coordinate system with the origin of the rectangular coordinate system $(xOy)$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar coordinate equation of line $l$ is $\rho (\cos \theta +\sin \theta )=4$.

(1) Find the maximum distance from any point $M$ on curve $C$ to line $l$.

(2) Let $P$ be a point on $l$, and the ray $OP$ intersects curve $C$ at point $R$. Another point $Q$ is on ray $OP$ and satisfies $|OP|\cdot |OQ|=|OR{{|}^{2}}$. Find the trajectory of moving point $Q$ as point $P$ moves on line $l$.

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