
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 C₁ as $$\begin{cases} x=1+ \sqrt {3}t \\ y=t\end{cases}$$ (where t is the parameter), and the polar coordinate equation of curve C₂ as ρ²(1+3sin²θ)=4, established with the origin of the rectangular coordinate system xOy as the pole and the positive semi-axis of x as the polar axis.

1. Find the general equation of curve C₁ and the rectangular coordinate equation of curve C₂.
2. If curve C₁ intersects with curve C₂ 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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