
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
For circles $C_1: (x-1)^2+(y-3)^2=9$ and $C_2: x^2+(y-2)^2=1$, let $M$ and $N$ be points on circles $C_1$ and $C_2$, respectively. Let $P$ be a point on the line $y=-1$. Find the minimum value of the sum of the distances from $P$ to $M$ and $P$ to $N$.

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