
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<sub>1</sub> defined by the equation $x^2+y^2-2x-4y-13=0$ and C<sub>2</sub> defined by $x^2+y^2-2ax-6y+a^2+1=0$ (where $a>0$) that are externally tangent to each other, and a line $l: (m+1)x+y-7m-7=0$ that is tangent to C<sub>2</sub>, find the value of $m$.

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