
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 line $l: kx - y + 1 + 2k = 0$ $(k \in R)$, the line $l$ intersects the negative semi-axis of $x$ at point $A$ and the positive semi-axis of $y$ at point $B$.

(1) Denote the area of $\Delta ABO$ as $S$, find the minimum value of $S$ and the equation of line $l$ at this time.

(2) The line $l$ passes through the fixed point $M$, find the equation of line $MO$ $(O$ is the origin of the coordinate$)$.

(3) When $k = -1$, the line $l$ intersects the $x$-axis at point $C$ and the $y$-axis at point $D$. Point $P$ is on the line $MO$ $(O$ is the origin of the coordinate$)$, find the minimum value of $|PC| + |PD|$.

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