
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 a polar coordinate system where the pole is the origin of a Cartesian coordinate system and the polar axis is the positive semi-axis of the x-axis, with both systems having the same length units, a curve C has the polar equation $ρ = 2(cos⁡θ + sin⁡θ)$.
(1) Find the rectangular equation of curve C.
(2) The line $l$: $x = \frac{1}{2}t, y = 1 + \frac{\sqrt{3}}{2}t$ (t is a parameter) intersects curve C at points A and B, and it intersects the y-axis at point E. Find the value of $|EA| + |EB|$.

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