
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 two-dimensional Cartesian coordinate system, the parametric equation of line $l$ is given by $\begin{cases} x=t+1 \\ y=\sqrt{3}t+1 \end{cases}$ (where $t$ is a parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive $x$-axis as the polar axis. The polar equation of curve $C$ is $3ρ^2\cos^2θ+4ρ^2\sin^2θ=12$.
(I) Write the polar equation of line $l$ and the Cartesian equation of curve $C$;
(II) Given that line $l'$ is parallel to line $l$ and passes through point $M(1,0)$, and intersects curve $C$ at points $A$ and $B$, find the length $|AB|$.

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