
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 polar coordinate system, the polar equation of curve $C\_1$ is $\rho =10\cos \theta$. Establish a Cartesian coordinate system with the pole $O$ as the origin and the non-negative semi-axis of the polar axis as the $x$-axis. The parametric equations of curve $C\_2$ are $\begin{cases} x=1+7t \ y=3+t \end{cases}$ ($t$ is the parameter).

(I) Find the rectangular equation of curve $C\_1$ and the general equation of curve $C\_2$;

(II) If curve $C\_1$ intersects curve $C\_2$ at points $A$ and $B$, and $P$ is a moving point on $C\_1$, find the maximum area of $\Delta PAB$.

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