
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 that the pole of the polar coordinate system coincides with the origin of the rectangular coordinate system, the polar axis coincides with the positive semi-axis of the $x$-axis, and the units of length are the same, the polar coordinate equation of the curve $C$ is $\rho =2(\cos \theta +\sin \theta )$.

(1) Find the rectangular coordinate equation of the curve $C$;

(2) The line $l$ with parameter equations $\begin{cases} & x=\frac{1}{2}t \\ & y=1+\frac{\sqrt{3}}{2}t \end{cases} (t \text{ is the parameter})$ intersects the curve $C$ at points $A$ and $B$, and intersects the $y$-axis at point $E$. Find the value of $\frac{1}{|EA|}+\frac{1}{|EB|}$.

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