
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 $O$ as the pole and the $x$-axis as the positive semi-axis. The polar coordinate equation of the curve $C$ is given as $\rho^2 - 4\rho\cos\theta - 6\rho\sin\theta + 12 = 0$.

1. Find the rectangular coordinate equation of the curve $C$.
2. A moving point $P$ on the curve $C$ is connected to the pole axis and the perpendicular foot $M$ and $N$ of the perpendicular line $\rho\cos\theta = -1$, respectively. Find the maximum value of $|PM| + |PN|$.

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