
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]


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Given the parametric equation of curve $C\_1$ is $\begin{cases} x=3\cos \alpha \ y=\sin \alpha \end{cases} (\alpha \text{ is the parameter})$, and the polar coordinate equation of curve $C\_2$ is $\rho \cos \left( \theta +\frac{\pi }{4} \right)=\sqrt{2}$.

(I) Find the rectangular coordinate equation of curve $C\_2$ and the maximum value of the distance $|OP|$ between the moving point $P$ on curve $C\_1$ and the coordinate origin $O$;

(II) If curve $C\_2$ intersects with curve $C\_1$ at points $A$ and $B$, and intersects with the $x$-axis at point $E$, find the value of $|EA|+|EB|$.

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