
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 two circles $C_1: (x-1)^2+(y+3)^2=1$ and $C_2: (x-a)^2+(y-b)^2=1$ are externally tangent, and a line $l: x-y-1=0$ passes through any point $P$ to draw tangents to circles $C_1$ and $C_2$ respectively, with the points of tangency being $M$ and $N$ such that $|PM|=|PN|$, calculate the value of $a+b$.

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