
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 rectangular coordinate system $xOy$, a pole coordinate system is established with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar coordinate equation of the curve C is $\rho^2 = \frac{8}{5 - 3\cos2\theta}$.

1. Find the rectangular coordinate equation of the curve C.
2. The line $l$ passing through the point M(1, 0) intersects the curve C at points A and B. If $\overrightarrow{AM} = 2\overrightarrow{MB}$, find the parametric equation of line $l$.

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