
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 equations of line $l$ as $$\begin{cases} x=1+3t \\ y= \frac {3}{2}t\end{cases}$$ and the polar equation of curve $C_1$ as $\rho = 2\sin\theta$ in the plane rectangular coordinate system $xOy$ with the origin as the pole and the positive semi-axis of $x$ as the polar axis, using the same unit length for both coordinate systems:

1. Find the standard equation of line $l$ and the rectangular equation of curve $C_1$.
2. If each point on curve $C_1$ is stretched horizontally and vertically by a factor of 3, forming curve $C_2$, find the maximum distance from a moving point $M$ on curve $C_2$ to line $l$.

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